AI generatedGeometry and measuresKS3 / GCSE

Volume of a frustum

Volume of a frustum.

  • Split a compound solid into familiar shapes.
  • Use perpendicular height for volume and slant height for a cone’s curved area.
  • Add volumes, or subtract a removed part. Give cubic units.

Example 1

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone4 cm2 cm5 cm5 cmDiagram not to scale
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.

Example 2

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone6 cm3 cm5 cm5 cmDiagram not to scale
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.

Your turn

Question 1

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone8 cm4 cm5 cm5 cmDiagram not to scale
Check answer
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.
Question 2

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone10 cm5 cm5 cm5 cmDiagram not to scale
Check answer
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.
Question 3

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone12 cm6 cm5 cm5 cmDiagram not to scale
Check answer
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.
Question 4

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone14 cm7 cm5 cm5 cmDiagram not to scale
Check answer
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.
Question 5

Find the volume of the frustum. The dashed top cone has been removed. Give an exact answer.

Frustum and removed cone16 cm8 cm5 cm5 cmDiagram not to scale
Check answer
The full height is the sum of the two marked heights.Calculate the removed cone.Subtract the removed volume.
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