# Volume of prisms

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

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.

$V = Ah$

$= 54 \times 12$

$= 648c{m^3}$

Question

Calculate the volume of the prism.

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.

$V = \pi {r^2}h$
$= \pi \times {4^2} \times 10$
$= 502.654...$
$= 500c{m^3}\,(to\,1\,s.f.)$