Question

The rectangular prism and rectangular pyramid below have the same volume. Determine the value of x, the length of the prism.

Answer 1

The answer is....... X=9in

Answer 2

`x`= 9
`in`

Step-by-step explanation

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

`V`=
`l` x
`b` x
`h`

We substitute the dimensions to obtain,

`V`= 6 x 3 x 12
`in^(3)`

The volume of the rectangular pyramid is,

`V`=
`(1)/(3)` x 6 x 12 x
`x`
`in^(3)`

Equating the two values gives,

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

We divide through by 6×12 to get,

`(x)/(3)` = 3

We solve for x to obtain,

`x` = 3 x 3

`x` = 9
`in`

Hope this helps! Happy Monday!