Volume of Prisms: Using a Formula

Contributed by:

NEO Thu, Feb 03, 2022 12:33 PM UTC

This pdf includes the following topics:-
The volume of Prisms: Using a Formula
Surface Area of Prisms
The volume of Rectangular Prisms
Examples and many more.

1. Volume of Prisms: Using a Formula Pathway
OPEN-ENDED
1
There are a variety of ways to create prisms and to figure out You will need
their volume.
• linking cubes
Part A • a camera (optional)
• pattern blocks
• Use linking cubes to make 3 different non-rectangular one-layer • centimetre cubes
bases. Then stack identical shapes on top of each base to build • a ruler
prisms. Take photos of your prisms if a camera is available. • a calculator
• Sketch the base of each prism you made.
Base of Prism 1: Base of Prism 2: Base of Prism 3: Re
emember
member
e.g., e.g., e.g.,
• Volume is the
amount of space a
shape takes up.
It is measured in
cubic units.
• Volume of a
rectangular prism 5
• Write the area of each base, in square units, and the number
area of base 3 height
of layers in each of your prisms.
h
Prism 1: Prism 2: Prism 3:
e.g., 5 square e.g., 5 square e.g., 5 square
units, 3 layers units, 4 layers units, 5 layers w
l
• How does the volume of each prism relate to the area of the base
and the number of layers?
e.g., The volume is the number of cubes, which is same as the product
of the base area and the height.
• Why does that make sense?
e.g., Each layer forms another equal group, and you multiply when
there are equal groups.
353
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Volume of Prisms: Using a Formula, Pathway 1

2. Part B
• Make 3 prisms of different heights by stacking pattern blocks.
Use only one type of pattern block for each prism. Sketch your
prisms, or sketch just the base and write the number of layers.
Tower 1: Tower 2: Tower 3:
e.g., e.g., e.g.,
• Describe the volume of each prism, using a triangle block as a unit.
Volume of Tower 1: Volume of Tower 2: Volume of Tower 3:
e.g., 5 green blocks e.g., 1 red block = 3 green e.g., 1 yellow block = 6 green
blocks, so 3 green blocks × 3 blocks, so 6 green blocks × 6
layers = 9 green blocks layers = 36 green blocks
• Estimate the volume of a triangle block, using centimetre cubes.
Explain your thinking.
e.g., I put 4 centimetre cubes in 2 rows of 2. The green block looks
like a bit less than 3 cm3, so my estimate is 2.5 cm3.
• Use your estimate for the volume of the triangle block to estimate
the volume of each prism you built.
Tower 1: Tower 2: Tower 3:
e.g., 2.5 cm3 × 5 green blocks e.g., 2.5 cm3 × 9 green blocks e.g., 2.5 cm3 × 36 green blocks
= 12.5 cm3 = 22.5 cm3 = 90 cm3
• Estimate the area of the base of each of your prisms and multiply
by the height. Then write the result.
Tower 1: Tower 2: Tower 3:
e.g., 2.5 cm2 × 5 cm e.g., 7.5 cm2 × 3 cm e.g., 15 cm2 × 6 cm
= 12.5 cm3 = 22.5 cm3 = 90 cm3
• What do you notice? Why does that make sense?
e.g., I got the same numbers. It makes sense since for rectangular
prisms the volume is the area of the base multiplied by the height.
Volume of Prisms: Using a Formula, Pathway 1 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

3. Volume of Prisms: Using a Formula Pathway
GUIDED
1
Abby creates chocolate treats in 2 shapes You will need
that are prisms.
• pattern blocks
Abby advertises that the 2 shapes have the • linking cubes
same volume. She knows that because she • a ruler
poured the same number of millilitres of • a calculator
chocolate into each mould.
Re
emember
member
• You can compare the volume of the prisms by looking at the shapes • Volume is the
amount of space a
and sizes in models made from pattern blocks. The area of the
shape takes up.
rhombus is twice the area of the triangle. If you cut the rhombus-
It is measured in
based prism in half and stack the pieces, it will look the same as the cubic units.
triangle-based prism.
• 1 mL of capacity 5
• You can also compare the volume of the prisms by calculating 1 cm3 of volume
the volume of each, using a formula: • Area of a
Volume 5 area of base 3 height parallelogram 5
base 3 height
or V 5 Abase 3 h
• Area of a triangle 5
This is the same as the formula for calculating the volume base 3 height 4 2
of rectangle-based prisms.
Volume of rhombus-based prism: Volume of triangle-based prism:
2.2 cm
2.2 cm
3.0 cm
6.0 cm
2.5 cm
The area of the base is
2.5 3 2.2 5 5.5 cm 2.
For 3 layers, the volume is
5.5 cm2 3 3.0 cm 5 16.5 cm 3. 2.5 cm
The area of the base is
2.5 3 2.2 4 2 5 2.75 cm 2.
For 6 layers, the volume is
2.75 cm2 3 6.0 cm 5 16.5 cm 3.
The volumes are equal.
355
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Volume of Prisms: Using a Formula, Pathway 1

4. Try These Re
emember
member
. a) Determine the area of the base of a • Assume that the
triangle pattern block. 2.2 cm thickness of each
2 pattern block is 1 cm.
e.g., 2.5 x 2.2 + 2 = 2.75 cm
________________________________ 2.5 cm
• You can figure
b) Determine the area of the base of each pattern block shown. out the height of a
(You can draw lines on the shapes to divide them into triangles.) prism by imagining
identical bases
2.5 cm stacked one on
top of another, or
2.5 cm stacked one behind
another.
2.5 cm
height
e.g., 2.75 × 3 = e.g., 2.75 × 2 = e.g., 2.75 × 6 =
8.25 cm2 5.5 cm2 16.5 cm2
height
c) What is the volume of a stack of 4 trapezoid blocks?
e.g., 8.25 cm2 × 4 cm = 33 cm3
________________________________
d) What is the volume of a stack of 4 blue rhombus blocks?
________________________________
e.g., 5.5 cm2 × 4 cm = 22 cm3
e) What is the volume of a stack of 2 hexagon blocks?
e.g., 16.5 cm2 × 2 cm = 33 cm3
________________________________
2. For each prism below, determine which surface is the base.
Figure out the area of the base, the height, and the volume.
a) b)
12 cm
8 cm
13 cm 3 cm
5 cm
3 cm
area of base: 3 × 8 + 2 = 12 cm2
____________________ area of base: 13 × 12 = 156 cm2
____________________
height of prism: ____________________
5 cm height of prism: ____________________
3 cm
12 × 5 = 60 cm3
volume of prism: ____________________ 156 × 3 = 468 cm3
volume of prism: ____________________
Volume of Prisms: Using a Formula, Pathway 1 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

5. 3. a) What is the volume of this prism? 4 cm 2 cm
4 cm
area of base: 4 x 4 + 4 x 2 = 24 cm2 4 cm
2 cm
8 cm
height of prism: __________________
4 cm
24 x 4 = 96 cm3
volume of prism: __________________
b) How does the volume of the prism change if you double the
height to 8 cm?
e.g., The volume doubles. It's 2 of the shapes stacked together.
c) How does the volume change if you double all of the
dimensions?
e.g., The volume is multiplied by 8. (That's 2 x 2 x 2.)
4. This eraser has the shape of a prism with a parallelogram base
that is not a rectangle.
5.5 cm
a) Why is the face with the writing not the base of the prism?
e.g., The base is one of the 2 parallelograms that is not a rectangle,
and the other 4 faces are rectangles.
e.g., about 1 cm
b) Estimate the height of the parallelogram. ___________________
e.g., about 2 cm
Estimate the height of the prism. ___________________
5. Suppose Marla made a wooden sculpture in the shape of a
parallelogram-based prism. It has a volume of about 150 cm3.
Sketch 2 possible drawings for the base and label the
dimensions. Determine the height of each prism.
Area of base: 10 × 5 = 50 cm2 Area of base: 10 × 3 = 30 cm2
Prism height: 3 cm Prism height: 5 cm
357
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Volume of Prisms: Using a Formula, Pathway 1

6. 6. Some of the measurements of a prism are in metres and some
are in centimetres. Why would you convert the measurements to
the same units?
e.g., If you multiplied the numbers without converting, the result would
not be meaningful; It wouldn't be square centimetres or square metres.
7. What is the volume of concrete needed to build these
steps?
1.3 m
height
e.g., bottom layer: 1.3 × 0.2 × 1 = 0.26 m2
of each
2nd layer: 1.3 × 0.2 × 0.75 = 0.2 m3 step:
3rd layer: 1.3 × 0.2 × 0.5 = 0.13 m3 20 cm
top layer: 1.3 × 0.2 × 0.25 = 0.07 m3
Total volume: 0.66 m3
depth of each step: 25 cm
8. These earrings are shaped like triangle-based prisms. What is the
volume of the 2 earrings?
e.g., The area of each base is 1 × 0.9 ÷ 2 = 0.45 cm2.
The height is 4 cm. The volume of 1 prism is 0.45 × 4 = 1.8 cm3.
The total volume is 2 × 1.8 = 3.6 cm3.
4 cm
0.9 cm
1 cm
9. Two other prisms have the same volume as the one shown
below. None of the prisms have a rectangular base. Sketch
2 possible bases for the other prisms and label the dimensions.
Determine the height of each prism. FYI
Learning how to
area of base: 6 × 5 ÷ 2 = 15 cm2
___________________ calculate volumes of
prisms will be useful
8 cm
___________________ for learning how to
5 cm height of prism:
8 cm calculate volumes of
cylinders later on.
6 cm 15 × 8 = 120 cm3
volume of prism: ___________________
Area of base: 2 × 15 ÷ 2 = 15 cm2 Area of base: 5 × 12 ÷ 2 = 30 cm2
Prism height: 8 cm Prism height: 4 cm
Volume of Prisms: Using a Formula, Pathway 1 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

7. Surface Area of Prisms Pathway
OPEN-ENDED
2
Aviva has 200 cm2 of fancy paper You will need
that she will use to cover a prism. I don’t want to
waste any paper • prisms from a set of
• Think of 2 different-shaped prisms that geometric solids
would each use all or most of Aviva’s paper overlapping it, so
• connecting faces
to cover the faces. Sketch the prisms and I’ll cut out pieces • 1 cm Grid Paper
label the dimensions you think are best for and glue them on. (BLM 12, optional)
each prism. • a ruler
• a calculator
(You might look at models and make a
sketch of each prism.
Or you might use connecting faces to make Re
emember
member
a model of each prism. • Area is measured in
Or you might sketch a net of each prism on square units.
grid paper.) • The base of a prism
is one of the 2 shapes
in the prism that may
not be a rectangle.
There are always
2 identical bases—
the top and bottom.
• The words base and
height can mean
Prism 1 sketch and dimensions: 2 different things
e.g., I think a square-based prism might work. in a prism.
The base can be a
polygon at the base
of the prism (B), or a
side length (b) of that
polygon.
The height can be
the full height of the
prism, or the height of
a base of the prism.
h
Prism 2 sketch and dimensions:
B
e.g., I think a triangle-based prism might work. h b
• A net is a 2-D picture
of a 3-D object that
is folded down.
359
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Surface Area of Prisms, Pathway 2

8. • Determine the surface area of each prism.
Use sketches to help you. surface area
the total area of all of
the faces of a shape
Prism 1 surface area:
e.g., The rectangle base is 5 × 5, so the top and
bottom areas together are 2 × 25 = 50 cm2.
Each side face has area 35 cm2. Since there are
4 of them, the area of all of the rectangles is
35 × 4 = 140 cm2.
So the total area is 50 + 140 = 190 cm2.
That's close to 200 cm2.
Prism 2 surface area:
e.g., The triangle base has an area of 24, so the top
and bottom together have an area of 48 cm2.
The side rectangles have areas of 36, 48, and 60, so
the total is 192 cm2. That's even closer to 200 cm2.
• Why did some pairs of faces have the same area?
I made this model using
e.g., The top and bottom always have the same area since in prisms 6 connecting faces
the top and bottom are identical. Sometimes if the base had other
equal sides, there would be other equal rectangular faces.
that are the same.
Surface Area of Prisms, Pathway 2 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

9. Surface Area of Prisms Pathway
GUIDED
2
Scientists know that the greater the You will need
area of the leaves of a plant, the
more sunlight can be absorbed for • prisms from a set of
growth. The surface area of plants geometric solids
• a calculator
can be complicated to figure out,
• a tape measure or a
but the surface area of shapes like
metre stick
prisms is easier to calculate.
Every prism has 2 bases with the
same area. It also has a number
surface area
of rectangular faces that might or
the total area of all of
might not have the same area. the faces of a shape
Re
emember
member
• Area is measured in
square units.
• To calculate the surface area of a 3-D shape, you add all of the areas.
• A net is a 2-D picture
For example, look at the triangle-based prism and its net, below. of a 3-D object that
is folded down.
4 6 = 24 cm2 3 6 = 18 cm2
5 cm
4 cm
6 cm
3 cm
5 6 = 30 cm2
3 4 2 2 = 12 cm 2
You can calculate the surface area (SA) of the triangle-based prism
like this:
SA 5 area of top base 1 area of bottom base 1 area of 3 rectangles
5 (4 3 3 4 2) 1 (4 3 3 1 2) 1 (6 3 4) 1 (6 3 3) 1 (6 3 5)
5 6 1 6 1 24 1 18 1 30
5 84 cm 2
For any prism: Re
emember
member
SA 5 2 3 area of base 1 area of all side rectangles • Area of a
The number of rectangles is always the same parallelogram 5
as the number of sides of the base. base 3 height
• Area of a triangle 5
• How many areas do you add to determine base 3 height 4 2
the area of a hexagon-based prism?
(oral) e.g., 8 areas for 8 faces
361
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Surface Area of Prisms, Pathway 2

10. Try These
Identify a base of each prism.
Figure out the area of the base. Re
emember
member
• The base of a
a) rectangle-based prism c) isosceles triangle-based prism is one of the
prism 2 shapes in the
prism that may not
10 cm be rectangles.
9 cm
8 cm There are always
2 identical bases—
the top and bottom.
3 cm
7 cm • The words base and
7 cm height can mean
12 cm
2 different things
area of base: area of base: in a prism.
The base can be a
e.g., 7 × 3 = 21 cm2
____________________ 12 × 8 ÷ 2 = 48 cm2
____________________
polygon at the base
of the prism (B), or a
b) parallelogram-based prism d) regular hexagon-based side length (b) of that
prism polygon.
The height can be
4 cm
the full height of the
5 cm prism, or the height
8 cm of a base of the
6 cm prism.
5.2 cm
h
4 cm
6 cm B
h b
area of base: area of base:
____________________
6 × 3 = 18 cm2 (6 × 5.2 ÷ 2) × 6 = 93.6 cm2
____________________
2. Calculate the areas of the faces that you did not identify as bases
in Question 1. (These faces should all be rectangles.)
a) c)
e.g., 2 faces: 3 × 9 = 27 cm2 2 faces: 7 × 10 = 70 cm2
2 faces: 7 × 9 = 63 cm2 1 face: 12 × 7 = 84 cm2
b) d)
2 faces: 6 × 8 = 48 cm2 6 faces: 6 × 4 = 24 cm2
2 faces: 5 × 8 = 40 cm2
Surface Area of Prisms, Pathway 2 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

11. 3. Calculate the surface area for each prism in Question 1.
a) c)
(2 × 21) + (2 × 27) + (2 × 63) (2 × 48) + (2 × 70) + 84
= 222 cm2 = 320 cm2
b) d)
(2 × 18) + (2 × 48) + (2 × 40) (2 × 93.6) + (6 × 24)
= 331.2 cm2
= 212 cm2
4. What is the surface area of each rectangular box?
Do not plan for any overlap.
a) b)
4 cm 6 cm
3 cm
7 cm
12 cm
10 cm
2 × (7 × 4) + 2 × (7 × 3) + 2 × (3 × 4) 2 × (10 × 6) + 2 × (10 × 12) + 2 × (12 × 6)
= 122 cm2 = 504 cm2
5. Suppose you need to know the surface area of a rectangular
classroom to paint it.
a) Estimate the surface area of the walls and ceiling of the
classroom. Do not include the floor. Show your thinking.
e.g., The room is about 8 m × 7 m, so the ceiling area is 56 m2.
The room is about 3 m high, so the walls' area is
(2 × 24) + (2 × 21) = 90 m2. The total surface area without the
floor is 146 m2.
b) If a 4 L can of paint covers 36 m2, about how many cans of
paint would you need?
146 ÷ 36 is about 4 cans of paint
363
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Surface Area of Prisms, Pathway 2

12. 6. Suppose you have one of the prisms below. You can calculate the
total surface area by doubling one area and tripling another, and
then adding them. What might the shape look like? Circle one.
7. To determine the surface area of some shapes, Aidan performed
the following calculations. What might each shape have been?
Use a name or a sketch.
a) 6 3 (7 3 7) c) 2 3 (5 3 12 4 2) 1 5 3 8 1 12 3 8 1
13 3 8
e.g., a cube, 7 by 7 by 7 e.g., a triangle-based prism with height
8, and base with height 12 and side
length 5
b) 2 3 (3 3 5) 1 2 3 (3 3 7) 1 2 3 (3 3 5) d) 2 3 (6 3 5.2 4 2) 1 (6 3 6) 3 5
e.g., a rectangular prism, 3 by 5 by 7 e.g., a regular hexagon-based prism
with base side of 6 and height of 5
8. You can use 20 linking cubes to make a 1-by-1-by-20 prism or
a 2-by-2-by-5 prism. They have the same volume.
Do they have the same surface area? How do you know?
No. e.g., One has a surface area of 82 square units, but the other
has a surface area of 48 square units.
9. A rectangular box has a surface area of 52 cm2.
What might the length, width, and height be?
e.g.,
FYI
The surface area of an
animal or a human is
an important factor in
keeping them neither
too hot nor too cold.
Surface Area of Prisms, Pathway 2 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

13. Volume of Rectangular Prisms Pathway
OPEN-ENDED
3
Rectangular prisms are very common shapes. You will need
• 50 linking cubes
• a calculator
• 3 classroom objects
in the shape of
rectangular prisms
• a ruler
Part A
• Use 50 linking cubes to build 3 rectangular prisms with different
dimensions. Use all or most of the cubes to build all 3 prisms.
• Record the number of cubes in the length, width, and height of each
prism, and the volume of the prism. volume
the amount of space
Prism 1: Prism 2: Prism 3: that a 3-D shape
e.g., 4 by 3 by 2, e.g., 1 by 1 by 10, takes up, measured
e.g., 4 by 2 by 2, in cubic units
volume is 16 cubic volume is 24 cubic volume is 10 cubic
units units units
• Repeat the task above for 3 more prisms.
Prism 4: Prism 5: Prism 6:
e.g., 2 by 2 by 2, e.g., 3 by 3 by 3, e.g., 2 by 5 by 1,
volume is 8 cubic volume is 27 cubic volume is 10 cubic
units units units
Re
emember
member
• Typical units of
volume are cubic
centimetres (cm3) and
• How can you predict the volume of the prism if you know the area of cubic metres (m3).
the base and the height? Tell why this makes sense. • Units for the area of
the base are likely
e.g., You can multiply the length and width to get the area of the base, square centimetres
and then multiply by the height to get the volume. Volume is a 3-D (cm2) or square
measurement so you use 3 dimensions. metres (m2).
• Area of a rectangle
5 length 3 width
365
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Volume of Rectangular Prisms, Pathway 3

14. Part B
Re
emember
member
• Find 3 objects in the classroom that are not too big and look like
• The volume of
rectangular prisms. (Or, imagine a rectangular box that your object
a linking cube is
would fit inside with very little extra space.) about 8 cm3.
• Measure and record the length, width, and height in centimetres.
• Predict the volume in cubic centimetres.
• Use cubes to check.
Object 1:
e.g., The stapler is about 18 cm × 4 cm × 5 cm high.
I predict 360 cm3 since 18 × 4 × 5 = 360.
My linking cube prism was 9 cubes × 2 cubes × 3 cubes = 54 cubes, and 8 × 54 = 432 cm3.
I knew it was a bit too high, so 360 seemed okay.
Object 2:
e.g., The whiteboard eraser is about 11 cm × 5 cm × 3 cm high.
I predict 165 cm3.
I built a 5 × 3 × 2 linking cube prism. It took 30 cubes and I knew it was bigger than the eraser.
30 × 8 = 240 cm3 and that is bigger, so I think 165 is good.
Object 3:
e.g., The stack of CDs is about 12 cm × 13 cm × 14 cm high. I predict 2184 cm3.
I didn't check with linking cubes since I'd need too many, but I did make a 6 × 7 layer and
realized there would be about 6 of them or a bit more; 6 × 7 × 6 = 252 and 8 × 252 = 2016, so
2184 seemed okay.
Volume of Rectangular Prisms, Pathway 3 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

15. Volume of Rectangular Prisms Pathway
GUIDED
3
The volume of a stack of books depends on the size of the pages and You will need
the height of the stack.
• centimetre cubes or
linking cubes
• a calculator
• a ruler
volume
the amount of space
that a 3-D shape
takes up, measured
• You can use centimetre cubes to model each stack. in cubic units
The short stack is made of
3 layers of 12 3 18 5 216 cubes.
Since this stack requires
3 3 216 5 648 centimetre cubes, Re
emember
member
the volume is 648 cm3. • Typical units of
volume are cubic
centimetres (cm3)
The tall stack with the same page size and cubic metres (m3).
can be modelled with • Units for the area of
6 layers of 216 cubes. the base are likely
Its volume is 6 3 216 5 1296 cm3. square centimetres
(cm2) or square
metres (m2).
The tall stack with a larger page size
can be modelled with
6 layers of 12 3 22 5 264 cubes.
Its volume is 6 3 264 5 1584 cm3.
The volume of a rectangular prism is calculated by multiplying
the area of the base by the height.
Volume 5 area of base 3 height or
V 5 Abase 3 h
367
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Volume of Rectangular Prisms, Pathway 3

16. Try These
. Each prism below is made of centimetre cubes. What is the
area of the base of the prism? What is the height of the prism
(the number of layers)? What is the volume?
a) c)
area of base: 6 cm2
____________________
area of base: 24 cm2
____________________
height of prism: ____________________
4 cm
height of prism: 3 cm
____________________
6 × 4 = 24 cm3
volume of prism: ____________________
24 × 3 = 72 cm3
volume of prism: ____________________
b) d)
area of base: 15 cm2
____________________
height of prism: ____________________
4 cm
area of base: 24 cm2
____________________
15 × 4 = 60 cm3
volume of prism: ____________________
height of prism: ____________________
5 cm
24 × 5 = 120 cm3
volume of prism: ____________________
Volume of Rectangular Prisms, Pathway 3 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

17. 2. a) Use centimetre cubes to build a prism with a 3-by-4 base
and a height of 2. Calculate the volume and explain your
reasoning.
e.g., The volume is 24 cm3 since the area of the base is 12 cm2 and
the height is 2 cm.
b) Turn the prism so the base is the 4-by-2 face.
What is the height? What is the volume?
e.g., The height is 3 cm and the volume is still 24 cm3.
c) Turn the prism again so the base is the 2-by-3 face.
What is the height? What is the volume?
e.g., The height is 4 cm and the volume is still 24 cm3.
3. A gift box has the given volume. What might its length, width, and
height be?
a) 500 cm3 b) 1350 cm3
e.g., 10 cm long, 10 cm e.g., 15 cm long, 9 cm
wide, and 5 cm high high, and 10 cm wide
4. A TV remote control in the shape of a rectangular prism has a
volume of 132 cm3. What might the height, width, and length be?
Show 2 possible solutions.
e.g., 22 cm long, 2 cm high, 3 cm wide;
11 cm long, 4 cm high, 3 cm wide
5. A wedding cake is made up of 3 tiers. Each tier is a
8 cm
square-based prism as shown and is 8 cm high.
What is the total volume of the cake? 15 cm 8 cm
bottom tier: 36 × 36 × 8 = 10 368 cm3 8 cm
middle tier: 25 × 25 × 8 = 5000 cm3 25 cm
top tier: 15 × 15 × 8 = 1800 cm3
Total volume = 17 168 cm3
36 cm
369
Copyright © 2012 by Nelson Education Ltd. Leaps and Bounds Volume of Rectangular Prisms, Pathway 3

18. 6. a) What is the volume of this cube?
10 × 10 × 10 = 1000 cm3
____________________
10 cm
b) What is the volume of the
remaining part of the cube after 10 cm
the smaller cube is taken out? 10 cm
10 cm
10 cm 3 cm
3 cm
10 cm 3 cm
10 × 10 × 10 - 3 × 3 × 3 = 973 cm3
7. Explain why it makes sense that this prism has a volume
of 42 cm3. 3.5 cm
e.g., The area of base is 4 × 3 = 12 cm2. If you multiply by 3, you get
3.0 cm
36 cm3 and if you multiply by 4, you get 48 cm3, so I went halfway 4.0 cm
between.
8. Using centimetre cubes, can you build more prisms with a volume
of 12 cm3 or with a volume of 14 cm3? Explain your thinking.
e.g., There are more prisms for 12 since it could be 1 × 1 × 12,
or 1 × 2 × 6, or 1 × 3 × 4, but for 14 it can only be 1 × 1 × 14 or 1 × 2 × 7.
9. The formula for the volume of a rectangular prism can be written
as V 5 Abase 3 h.
Why is the formula below another formula for the volume of
a rectangular prism?
V 5 l 3 w 3 h, where l is the length of the base, w is the width of
the base, and h is the height of the prism
FYI
Learning how to
e.g., The area of the base is l × w, so you can just say that instead calculate volumes of
rectangular prisms
of Abase before you multiply by the height. will help you learn
formulas for other
prisms, too.
Volume of Rectangular Prisms, Pathway 3 Leaps and Bounds Copyright © 2012 by Nelson Education Ltd.

Book a Trial Class

Download