Contributed by:

This pdf contains the problem of rectangular prisms with step-by-step solutions. A rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles.

1.
® Name:

Date:

Finding the Volume of Rectangular Prisms VOL 1

Instructions: Find the volume of each rectangular prism by multiplying the area of the ‘base’

times the length the base has been extended. (Don’t forget about the units!)

1 2

10 in 2 in

5m

8m

7 in

6m

Area = 5 × 6 = 30 m2 Area = 2 × 7 = 14 in2

of Base

of Base

Volume = 30 m2 × 8 m = 240 m3 Volume = 14 in2 × 10 in = 140 in3

3 4

5 cm

20 cm 9 ft

12 ft

5 cm

4 ft

Area = 5 × 5 = 25 cm2 Area = 9 × 4 = 36 ft2

of Base

of Base

Volume = 25 cm2 × 20 cm = 500 cm3 Volume = 36 ft2 × 12 ft = 432 ft3

5 6

3 in 4m

9 in

6m

5 in 4m

Area = 3 × 5 = 15 in2 Area = 4 × 4 = 16 m2

of Base of Base

Volume = 15 in2 × 9 in = 135 in3 Volume = 16 m2 × 6 m = 96 m3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

Date:

Finding the Volume of Rectangular Prisms VOL 1

Instructions: Find the volume of each rectangular prism by multiplying the area of the ‘base’

times the length the base has been extended. (Don’t forget about the units!)

1 2

10 in 2 in

5m

8m

7 in

6m

Area = 5 × 6 = 30 m2 Area = 2 × 7 = 14 in2

of Base

of Base

Volume = 30 m2 × 8 m = 240 m3 Volume = 14 in2 × 10 in = 140 in3

3 4

5 cm

20 cm 9 ft

12 ft

5 cm

4 ft

Area = 5 × 5 = 25 cm2 Area = 9 × 4 = 36 ft2

of Base

of Base

Volume = 25 cm2 × 20 cm = 500 cm3 Volume = 36 ft2 × 12 ft = 432 ft3

5 6

3 in 4m

9 in

6m

5 in 4m

Area = 3 × 5 = 15 in2 Area = 4 × 4 = 16 m2

of Base of Base

Volume = 15 in2 × 9 in = 135 in3 Volume = 16 m2 × 6 m = 96 m3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

2.
® Name:

Date:

Finding the Volume of Triangular Prisms VOL 2

Instructions: Find the volume of each triangular prism by multiplying the area of the ‘base’ times

the length the base has been extended. (Don’t forget about the units!)

1 2

10 m

4 in

12 m 8 in

9m

4 in

90

Area = 1 (9 × 10) = = 45 m2 Area =

1

(4 × 4) =

16

= 8 in2

of Base 2 2 of Base 2 2

Volume = 45 m2 × 12 m = 540 m3 Volume = 8 in2 × 8 in = 64 in3

3 4

4 cm 8 ft

18 cm

12 ft

6 cm

5 ft

1 24 40

Area = (6 × 4) = = 12 cm2 1

of Base 2 2 Area = (5 × 8) = = 20 ft2

of Base 2 2

Volume = 12 cm2 × 18 cm = 216 cm3 Volume = 20 ft2 × 12 ft = 240 ft3

5 6

7m 10 in

9m 14 in

4m 9 in

1 28 1 90

Area = (4 × 7) = = 14 m2 Area = (9 × 10) = = 45 in2

of Base 2 2 of Base 2 2

Volume = 14 m2 × 9 m = 126 m3 Volume = 45 in2 × 14 in = 630 in3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

Date:

Finding the Volume of Triangular Prisms VOL 2

Instructions: Find the volume of each triangular prism by multiplying the area of the ‘base’ times

the length the base has been extended. (Don’t forget about the units!)

1 2

10 m

4 in

12 m 8 in

9m

4 in

90

Area = 1 (9 × 10) = = 45 m2 Area =

1

(4 × 4) =

16

= 8 in2

of Base 2 2 of Base 2 2

Volume = 45 m2 × 12 m = 540 m3 Volume = 8 in2 × 8 in = 64 in3

3 4

4 cm 8 ft

18 cm

12 ft

6 cm

5 ft

1 24 40

Area = (6 × 4) = = 12 cm2 1

of Base 2 2 Area = (5 × 8) = = 20 ft2

of Base 2 2

Volume = 12 cm2 × 18 cm = 216 cm3 Volume = 20 ft2 × 12 ft = 240 ft3

5 6

7m 10 in

9m 14 in

4m 9 in

1 28 1 90

Area = (4 × 7) = = 14 m2 Area = (9 × 10) = = 45 in2

of Base 2 2 of Base 2 2

Volume = 14 m2 × 9 m = 126 m3 Volume = 45 in2 × 14 in = 630 in3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

3.
® Name:

Date:

Finding the Volume of Cylinders VOL 3

Instructions: Find the volume of each cylinder by multiplying the area of the ‘base’ times the

length the base has been extended. (Use 3.14 for Pi and don’t forget about the units!)

1 2

3m

6m

20 in 5 in

Area = π × (3 m)2 = 3.14 × 9 m2 Area = π × (5 in)2 = 3.14 × 25 in2

of Base of Base

= 28.26 m2 = 78.5 in2

V = 28.26 m2 × 6 m = 169.56 m3 V = 78.5 in2 × 20 in = 1,570 in3

6m

3 4

7m

25 cm 4 cm

Area = π × (4 cm)2 = 3.14 × 16 cm2 Area = π × (6 m)2 = 3.14 × 36 m2

of Base of Base

= 50.24 cm2 = 113.04 m2

V = 50.24 cm2 × 25 cm = 1,256 cm3 V = 113.04 m2 × 7 m = 791.28 m3

1 in

5 6

2 cm

8 in

10 cm

Area = π × (1 in)2 = 3.14 × 1 in2 Area = π × (2 cm)2 = 3.14 × 4 cm2

of Base of Base

= 3.14 in2 = 12.56 cm2

V = 3.14 in2 × 8 in = 25.12 in3 V = 12.56 cm2 × 10 cm = 125.6 cm3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

Date:

Finding the Volume of Cylinders VOL 3

Instructions: Find the volume of each cylinder by multiplying the area of the ‘base’ times the

length the base has been extended. (Use 3.14 for Pi and don’t forget about the units!)

1 2

3m

6m

20 in 5 in

Area = π × (3 m)2 = 3.14 × 9 m2 Area = π × (5 in)2 = 3.14 × 25 in2

of Base of Base

= 28.26 m2 = 78.5 in2

V = 28.26 m2 × 6 m = 169.56 m3 V = 78.5 in2 × 20 in = 1,570 in3

6m

3 4

7m

25 cm 4 cm

Area = π × (4 cm)2 = 3.14 × 16 cm2 Area = π × (6 m)2 = 3.14 × 36 m2

of Base of Base

= 50.24 cm2 = 113.04 m2

V = 50.24 cm2 × 25 cm = 1,256 cm3 V = 113.04 m2 × 7 m = 791.28 m3

1 in

5 6

2 cm

8 in

10 cm

Area = π × (1 in)2 = 3.14 × 1 in2 Area = π × (2 cm)2 = 3.14 × 4 cm2

of Base of Base

= 3.14 in2 = 12.56 cm2

V = 3.14 in2 × 8 in = 25.12 in3 V = 12.56 cm2 × 10 cm = 125.6 cm3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

4.
® Name:

Date:

Finding the Volume of Spheres and Cones - Set 1 G-VOL 4

Instructions: Find the volume of each sphere or cone using the formulas given. (Use 3.14 for Pi,

round answers to two decimal places, and don’t forget about the units!)

1

Formula for a Sphere

4 2m

Volume = × π × r3

3

Formula for a Cone 4

V= × 3.14 × (2 × 2 × 2) m3

1 3

Volume = × h × π × r2

3 4 × 25.12 m3

= = 33.49 m3

3

2 3 9m

3 cm

7m

4

V= × 3.14 × (3 × 3 × 3) cm3 1

3 V= × 9 m × 3.14 × (7 × 7) m2

3

4 × 84.78 cm3

= = 113.04 cm3 = 3 m x 153.86 m2 = 461.58 m3

3

4 5

6 in

4 km

2 in

1 4

V= × 6 in × 3.14 × (2 × 2) in2 V= × 3.14 × (4 × 4 × 4) km3

3 3

= 2 in × 12.56 in2 = 25.12 in3 4 × 200.96 km3

= = 267.95 km3

3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

Date:

Finding the Volume of Spheres and Cones - Set 1 G-VOL 4

Instructions: Find the volume of each sphere or cone using the formulas given. (Use 3.14 for Pi,

round answers to two decimal places, and don’t forget about the units!)

1

Formula for a Sphere

4 2m

Volume = × π × r3

3

Formula for a Cone 4

V= × 3.14 × (2 × 2 × 2) m3

1 3

Volume = × h × π × r2

3 4 × 25.12 m3

= = 33.49 m3

3

2 3 9m

3 cm

7m

4

V= × 3.14 × (3 × 3 × 3) cm3 1

3 V= × 9 m × 3.14 × (7 × 7) m2

3

4 × 84.78 cm3

= = 113.04 cm3 = 3 m x 153.86 m2 = 461.58 m3

3

4 5

6 in

4 km

2 in

1 4

V= × 6 in × 3.14 × (2 × 2) in2 V= × 3.14 × (4 × 4 × 4) km3

3 3

= 2 in × 12.56 in2 = 25.12 in3 4 × 200.96 km3

= = 267.95 km3

3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

5.
® Name:

Date:

Finding the Volume of Spheres and Cones - Set 2 G-VOL 5

Instructions: Find the volume of each sphere or cone using the formulas given. (Use 3.14 for Pi,

round answers to two decimal places, and don’t forget about the units!)

1 8m

Formula for a Sphere

4

Volume = × π × r3

3 3m

Formula for a Cone

1

V= × 8 m × 3.14 × (3 × 3) m2

1 3

Volume = × h × π × r2

3 = 2.67 m × 28.26 m2 = 75.45 m3

2 3 in 3

8 cm

2 in

1 4

V= × 3 in × 3.14 × (2 × 2) in2 V= × 3.14 × (8 × 8 × 8) cm3

3 3

= 1 in × 12.56 in2 = 12.56 in3 4 × 1607.68 cm3

= = 2,143.57 cm3

3

4 5

9 in

1.5 m

2.5 in

4

V= × 3.14 × (1.5 × 1.5 × 1.5) m3 1

3 V= × 9 in × 3.14 × (2.5 × 2.5) in2

3

4 × 10.598 m3

= = 14.13 m3 = 3 in x 19.625 in2 = 58.88 in3

3

Volume • mathantics.com © 2016 Math Plus Motion, LLC

Date:

Finding the Volume of Spheres and Cones - Set 2 G-VOL 5

Instructions: Find the volume of each sphere or cone using the formulas given. (Use 3.14 for Pi,

round answers to two decimal places, and don’t forget about the units!)

1 8m

Formula for a Sphere

4

Volume = × π × r3

3 3m

Formula for a Cone

1

V= × 8 m × 3.14 × (3 × 3) m2

1 3

Volume = × h × π × r2

3 = 2.67 m × 28.26 m2 = 75.45 m3

2 3 in 3

8 cm

2 in

1 4

V= × 3 in × 3.14 × (2 × 2) in2 V= × 3.14 × (8 × 8 × 8) cm3

3 3

= 1 in × 12.56 in2 = 12.56 in3 4 × 1607.68 cm3

= = 2,143.57 cm3

3

4 5

9 in

1.5 m

2.5 in

4

V= × 3.14 × (1.5 × 1.5 × 1.5) m3 1

3 V= × 9 in × 3.14 × (2.5 × 2.5) in2

3

4 × 10.598 m3

= = 14.13 m3 = 3 in x 19.625 in2 = 58.88 in3

3

Volume • mathantics.com © 2016 Math Plus Motion, LLC