Volume of prisms

A prism is a solid with a uniform cross-section. This means that no matter where it is sliced along its length, the cross section is the same size and shape (congruent).

Diagram of a cylinder split into slices

A well-known example of a prism is a cylinder and you can see from the image above that the front face (cross-section) is the same size of circle no matter where you slice it.

V = Ah

Question

Calculate the volume of the prism.

Hexagonal prism with a length of 12cm and a face area of 54cm≤

V = Ah

= 54 \times 12

= 648c{m^3}

Question

Calculate the volume of the prism.

Triangular prism with dimensions of 12cm x 6cm x 4cm

This shape is a triangular prism so the area of the cross-section is the area of a triangle.

Area of the triangle:

A = \frac{1}{2}bh

= \frac{1}{2} \times 6 \times 4

= 12c{m^2}

Volume of the prism:

V = Ah

= 12 \times 12

= 144c{m^3}

Volume of a cylinder

The formula for the volume of a cylinder (circular prism) is derived from the volume of a prism, where r is the radius and h is the height/length.

V = Ah

Since the area of a circle = \pi {r^2}, then the formula for the volume of a cylinder is:

V = \pi {r^2}h

Question

Calculate the volume of the cylinder shown.

Give your answer correct to 1 significant figure.

Diagram of a cylinder with a height of 10cm and a radius of 4cm

V = \pi {r^2}h

= \pi  \times {4^2} \times 10

= 502.654...

= 500c{m^3}\,(to\,1\,s.f.)