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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

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