Question

A prism whose bases are equilateral triangles is inscribed in a cylinder of radius 2 and height 5. What is the volume of the prism?

Answer 1

The volume of the prism is
`15√(3)\ units^(3)`

Explanation:

we know that

The volume of the prism is equal to

`V=Bh`

where

B is the area of the equilateral triangle of the base

h is the height of the prism

step 1

Find the area of the base of the prism

The formula to calculate the area of a triangle by SAS (side-angle-side) is equal to

`A=(1)/(2)(a)(b)sin(C)`

so

The area of the equilateral triangle of the base is

`A=3*((1)/(2)(r)(r)sin(120\°))`

we have

`r=2\ units`

substitute

`A=3*((1)/(2)(2)(2)(√(3))/(2))`

`A=3√(3)\ units^(2)`

step 2

Find the volume of the prism

`V=Bh`

we have

`B=3√(3)\ units^(2)`

`h=5\ units`

substitute

`V=3√(3)*5=15√(3)\ units^(3)`