AI generatedGeometry and measuresKS3 / GCSE

Surface area of a composite solid

Surface area of a composite solid.

  • Surface area counts only surfaces exposed on the outside.
  • Exclude faces where two solids join; include an exposed base.
  • For a cone, use the slant height in πrl. Give square units.

Example 1

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius2 cm5 cmDiagram not to scale
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

Example 2

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius3 cm5 cmDiagram not to scale
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

Your turn

Question 1

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius4 cm5 cmDiagram not to scale
Check answer
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

Question 2

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius5 cm5 cmDiagram not to scale
Check answer
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

Question 3

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius6 cm5 cmDiagram not to scale
Check answer
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

Question 4

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius7 cm5 cmDiagram not to scale
Check answer
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

Question 5

A cylinder is topped with a hemisphere of the same radius. Find the total exposed surface area, including the circular base. Give an exact answer.

Cylinder with a hemisphere of the same radius8 cm5 cmDiagram not to scale
Check answer
Add only exposed surfaces.Substitute the common radius and cylinder height.

The joined circle is internal, so it contributes no exposed area.

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