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Frequently Asked Questions

How do you find the volume of a prism?


In a similar way that area is the number of square units that a shape covers, volume is a measure of the amount of space a solid occupies, measured in cubic units.

Consider a grid measuring 3 by 4 units.

It can be seen that 12 cube units are required to complete one layer, and so a box with a base measuring 3 by 4 units and measuring 5 units tall, would have 5 layers of 12 cubes, i.e. 12 × 5 = 60 units³.

Area is measured in square units, so when we speak of the area of non-rectangular shapes we are suggesting an equivalent. Hence if a cylinder had a base with an area of 12 square units, we are saying that the base (circle) would cover exactly the same area as 12 square units. If we then knew that it was 5 units (layers) tall, we could calculate the volume; i.e. 60 cubic units.

We call any solid that has the same (constant) cross section throughout its length a prism and this leads to a generalisation that the volume of a prism, V, is given by V = Abase × h, where h is the height/length of the prism.