Question

be rectangular prism and rectangular pyramid have the same volume. determine the value of x, the height of the pyramid.

Answer 1

using this for points, sorry.

Explanation:

Answer 2

ANSWER


`x= 9 \: in`

EXPLANATION

The volume of a rectangular prism is given by the formula,


`V = l * b * h`
We substitute the dimensions to obtain,


`V = 6 * 3 * 12 \: {in}^(3)`

The volume of the rectangular pyramid is,


`V = (1)/(3) * 6 * 12 * x \: {in}^(3)`

Equating the two volumes gives,


`(1)/(3) * 6 * 12 * x = 6 * 3 * 12`

We divide through by 6×12 to get,


`(x)/(3)=3`

We solve for x to obtain,


`x = 3 * 3`


`x = 9 \: in`