Volume of Prisms and Cylinders
Grade 4The prism rule
A prism is a 3D shape with the same cross-section all the way along its length. Cuboids, cylinders, triangular prisms — they are all prisms. The volume is always:
For a cylinder specifically, the cross-section is a circle, so:
Identifying the cross-section
The key step is finding the right cross-section — the face that stays constant along the length. For a triangular prism lying on its side, the cross-section is the triangle at the end, not the rectangular face.
Worked example
Try this one
A solid sphere has a radius of \( 3 \) cm.
Calculate the volume of the sphere. Give your answer to \( 1 \) decimal place. [3]
Use the sphere volume formula, which involves the cube of the radius.
Ask yourself: 'have I cubed the radius rather than squaring it?' Work out \( r^3 \) first, then apply the \( \dfrac{4}{3}\pi \) factor.
