Surface Area and Volume of Composite Shapes

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NEO Thu, Feb 03, 2022 12:28 PM UTC

This pdf shows how to find the surface area and volume of composite shapes step by step with examples for better explanation.

1. Composite Solids

2. Example Question 1 Composite Solids
An aeronautical engineer designs a small component part made of copper, that is
to be used in the manufacturer of an aircraft. The part consists of a cone that sits
on top of a cylinder as shown in the diagram below. Find the volume of the part.
(Leave your answer in terms of ).
Volume of cone = 1/3 r2h
= 1/3 x  x 42 x 9
9 cm
= 48 cm3
8 cm
Vol/Cap
Volume of cylinder = r2h
=  x 42 x 6
6 cm = 96 cm3
Total volume = 48 + 96 = 144 cm3

3. Example Question 2 Composite Solids
The shape below is composed of a solid metal cylinder capped with a solid metal
hemi-sphere as shown. Find the volume of the shape. (to 3 sig fig)
Volume of hemi-sphere = 2/3 r3
= 2/3 x  x 33
= 18 m3
6m
Volume of cylinder = r2h
4m =  x 32 x 4
= 36 m3
Total volume = 18 + 36 = 54 m3
= 170 m3

4. Example Question 3 Composite Solids
The diagram below shows a design for a water tank. The water tank consists of a
cylinder capped with a hemi-spherical dome. Find the capacity of the water tank.
(Give your answer in litres to 2 sig fig).
Capacity of hemi-sphere = 2/3 r3
= 2/3 x  x 33
6m = 18 m3
Capacity of cylinder = r2h
5m =  x 32 x 5
= 45 m3
1 000
1 000 000cm
cm3 3 Total capacity = 18 + 45 = 63 m3
= 63 000 000 cm3
10 cm
100 cm 1 = 63 000 litres
litre
10
100cm
cm = 200 000 litres (2 sig fig)
10 cm
100 cm

5. Example Question 4 Composite Solids
A solid shape is composed of a cylinder with a hemi-spherical
14 cm base and a conical top as shown in the diagram. Calculate the
volume of the shape. (answer to 2 sig fig)
Volume of cone = 1/3 x r2h
= 1/3 x  x 62 x 14
= 168 cm3
Volume of cylinder = r2h
=  x 62 x 40
40 cm
= 1440 cm3
Volume of hemi-sphere = 2/3 r3
= 2/3 x  x 63
= 144 cm3
12 cm
Total volume = 168 + 1440 + 144 = 1752 cm3
= 5500 cm3

6. Question 1 Composite Solids
An aeronautical engineer designs a small component part made of copper, that is
to be used in the manufacturer of an aircraft. The part consists of a cone that sits
on top of a cylinder as shown in the diagram below. Find the volume of the part.
(Leave your answer in terms of ).
Volume of cone = 1/3 r2h
= 1/3 x  x 52 x 12
12 cm
= 100 cm3
Volume of cylinder = r2h
10 cm
=  x 52 x 6
6 cm = 150 cm3
Total volume = 100 + 150 = 250 cm3

7. Question 2 Composite Solids
The shape below is composed of a solid metal cylinder capped with a solid metal
hemi-sphere as shown. Find the volume of the shape. (to 2 sig fig)
Volume of hemi-sphere = 2/3 r3
= 2/3 x  x 93
= 486 cm3
18 cm
Volume of cylinder = r2h
10 =  x 92 x 10
cm
= 810 m3
Total volume = 486 + 810 = 1296 cm3
= 4100 cm3

8. Question 3 Composite Solids
The diagram below shows a design for a water tank. The water tank consists of a
cylinder capped with a hemi-spherical dome. Find the capacity of the water tank.
(Give your answer in litres to 3 sig fig).
Capacity of hemi-sphere = 2/3 r3
= 2/3 x  x 63
12 m = 144 m3
Capacity of cylinder = r2h
10m =  x 62 x 10
= 360 m3
1 000
1 000 000cm
cm3 3 Total capacity = 144 + 360 = 504 m3
= 504 000 000 cm3
10 cm
100 cm 1 = 504 000 litres
litre = 1 580 000 litres (3 sig fig)
10
100cm
cm
10 cm
100 cm

9. Question 4 Composite Solids
A solid shape is composed of a cylinder with a hemi-spherical
9 cm base and a conical top as shown in the diagram. Calculate the
volume of the shape. (answer to 2 sig fig)
Volume of cone = 1/3 x r2h
= 1/3 x  x 32 x 9
= 27 cm3
Volume of cylinder = r2h
20 cm =  x 32 x 20
= 180 cm3
Volume of hemi-sphere = 2/3 r3
= 2/3 x  x 33
= 18 cm3
6 cm
Total volume = 27 + 180  + 18 = 225  cm3
= 710 cm3

10. Example Questions Surface Area
Worksheets

11. Questions Surface Area

12. Example Questions Volume/Capacity

13. Questions Volume/Capacity

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