Volume of Prisms and Cylinders

A prism is a solid with two identical, parallel bases joined by edges of equal length; that shared length is its height, the distance between the bases. A triangular prism has triangles at each end. A cylinder is not strictly a prism, because its base is a circle rather than a polygon, but it has the same two-identical-ends shape, so its volume works the same way.

Multiply the area of the base by the height: V = B × h. First find the area of one of the identical end faces, then multiply by the distance between them. A prism with a base area of 20 cm² and a height of 3 cm has a volume of 20 × 3 = 60 cm³. Volume is always in cubic units.

Find the area of the triangular end with ½ × base × height, then multiply by the prism’s length. The video’s triangle has area 6 cm² and the prism is 5 cm long, so the volume is 6 × 5 = 30 cm³. A triangle of base 10 cm and height 5 cm has area 25 cm²; on an 8 cm prism that is 200 cm³.

The base is a circle, so multiply its area by the height: V = πr²h. A can with a radius of 2 cm and a height of 5 cm has volume π × 2² × 5 = 20π cm³, about 62.8 cm³ using 3.14 for π. A cylinder with radius 3 cm and height 4 cm has volume 36π cm³. Leave the answer in terms of π unless asked for a decimal.

Halve the diameter to get the radius first, then use V = πr²h. A cylinder with a diameter of 10 cm has a radius of 5 cm, so with a height of 5 cm its volume is π × 5² × 5 = 125π cm³. To turn cubic centimetres into litres, divide by 1,000: 125π cm³ is about 393 cm³, or 0.39 litres.