Find the volume of the prism if the lateral area is 720 square centimetre?

Question

in a regular prism, the ratio of an edge of the base to the height of the prism is 1:5. find the volume of the prism if the lateral area is 720 square centimetre

Answer 1

The ratio of an edge of the base to the height of the prism is 1:5.

And the lateral area is 720 square centimeter.

Lateral Area of a Right Prism (LA) = ph,

where p is perimeter of the base, and h is height of prism,

Let the perimeter of the base is 'x' and the height of prism is '5x'

i.e. (x)(5x) = 720

5x² = 720

Divide each side by 5.

x² = 144

Take square root each side.

Then x = 12

Therefore the perimeter of the base is 12. and the height of prism is 5(12) =60

The volume of the prism is V = Bh (where B is base area and h is height of prism)

i.e.Triangle area is B = (1/2)(bh) = (1/2)(12)(60) = 360 square centimeter.

The volume of the prism is V = (360)(60) = 21,600 cube centimeter.