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:
Volume = cross-sectional area × length
For a cylinder specifically, the cross-section is a circle, so:
Volume of cylinder = πr²h
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.
Sketch the shape and mentally "slice" it to reveal the cross-section face. Calculate that area, then multiply by the depth or length.
Worked example
EXAMPLE
A triangular prism has a right-angled triangular cross-section with legs 6 cm and 8 cm. The prism is 15 cm long. Find the volume.
Cross-sectional area = ½ × 6 × 8 = 24 cm². Volume = 24 × 15 = 360 cm³.
