Measurement

UK Secondary (7-11)

Surface Area of Complex Composite Solids

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?

- Break the solid in to more familiar solids (e.g. a cylinder and two cones).
- Draw a net of each solid.
- Only include faces which are on the surface of the composite solid.

- Calculate the area of each net
- Add up the area of all the nets.

A

- Break the solid in to more familiar solids (e.g. a cylinder and two cones).
- Draw a net of each solid.
- Include all faces on each solid.

- Calculate the area of each net
- Add up the area of all the nets.

B

- Break the solid in to more familiar solids (e.g. a cylinder and two cones).
- Calculate the volume of each solid.
- Add up the volume of all the solids.

C

- Break the solid in to more familiar solids (e.g. a cylinder and two cones).
- Draw a net of each solid.
- Only include faces which are on the surface of the composite solid.

- Calculate the area of each net
- Add up the area of all the nets.

A

- Break the solid in to more familiar solids (e.g. a cylinder and two cones).
- Draw a net of each solid.
- Include all faces on each solid.

- Calculate the area of each net
- Add up the area of all the nets.

B

- Break the solid in to more familiar solids (e.g. a cylinder and two cones).
- Calculate the volume of each solid.
- 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

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