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In this pdf, we will learn how to calculate the volume of Composite Solids. To calculate the volume of a composite solid, simply split it into smaller solids and calculate their separate volumes. The volumes of each of the individual solids are then added together to give the total volume of the composite solid.

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

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

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

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

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

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

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

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

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

Worksheets

11.
Questions Surface Area

12.
Example Questions Volume/Capacity

13.
Questions Volume/Capacity