UK Secondary (7-11)
Surface Area of Complex Composite Solids

Interactive practice questions

The figure shows a cylinder of radius $4$4cm, and its height is double the radius. On the top and bottom of the cylinder are cones with radii and height both also equal to $4$4.

a

How can we calculate the Surface Area of this complex composite solid?

1. Break the solid in to more familiar solids (e.g. a cylinder and two cones).
2. Draw a net of each solid.
• Only include faces which are on the surface of the composite solid.
3. Calculate the area of each net
4. Add up the area of all the nets.
A
1. Break the solid in to more familiar solids (e.g. a cylinder and two cones).
2. Draw a net of each solid.
• Include all faces on each solid.
3. Calculate the area of each net
4. Add up the area of all the nets.
B
1. Break the solid in to more familiar solids (e.g. a cylinder and two cones).
2. Calculate the volume of each solid.
3. Add up the volume of all the solids.
C
1. Break the solid in to more familiar solids (e.g. a cylinder and two cones).
2. Draw a net of each solid.
• Only include faces which are on the surface of the composite solid.
3. Calculate the area of each net
4. Add up the area of all the nets.
A
1. Break the solid in to more familiar solids (e.g. a cylinder and two cones).
2. Draw a net of each solid.
• Include all faces on each solid.
3. Calculate the area of each net
4. Add up the area of all the nets.
B
1. Break the solid in to more familiar solids (e.g. a cylinder and two cones).
2. Calculate the volume of each solid.
3. Add up the volume of all the solids.
C
b

Which option below shows the solid broken in to its nets? (Measurements are rounded to one decimal place where appropriate.)

A

B

C

D

A

B

C

D
Easy
Approx 2 minutes

Find the surface area of the composite figure shown, which consists of a cone and a hemisphere joined at their bases.

Round your answer to two decimal places.

Find the surface area of the composite figure shown.

Round your answer to two decimal places.

If a spherical ball with a radius of $3.7$3.7cm fits exactly inside a cylinder, what is the surface area of the cylinder?

Round your answer to one decimal place.