AI generatedGeometry and measuresKey Stage 3

Volume of a prism with a compound cross-section

Volume of a prism with a compound cross-section.

  • 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

A prism has this constant cross-section and length 4 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.

Example 2

A prism has this constant cross-section and length 5 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.

Your turn

Question 1

A prism has this constant cross-section and length 6 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Check answer
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.
Question 2

A prism has this constant cross-section and length 7 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Check answer
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.
Question 3

A prism has this constant cross-section and length 8 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Check answer
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.
Question 4

A prism has this constant cross-section and length 9 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Check answer
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.
Question 5

A prism has this constant cross-section and length 10 cm. Find its volume.

L-shaped cross-section; lengths in cmDashed lines show the removed rectangle; lengths in cm.
Check answer
Subtract the cut-out rectangle from the full rectangle.Multiply cross-sectional area by prism length.
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