Question

The solid surface area is equal to the solid volume. Find the value of x? The measurements of the rectangular prism is 11 inches long and 3 inches wide. Height is not listed.

Helping my son out with his math problem. I know it is length x width x height but the height is not listed. Not sure how to help him on this one. Thank you.

Answer 1

I'm guessing that `x` is the missing height value.

See the solution below, which shows `x=13.2` inches.

Explanation:

Volume:

`V="length"xx"width"xx"height"=11xx3xx x=33x`

Surface area:

`SA=2("length"xx"width")+2("width"xx"height")+2("length"xx"height")`
= `2[("length"xx"width")+("width"xx"height")+("length"xx"height")]`

= `2((11xx3)+(3xx x)+(11xx x)`

= `2(33+3x+11x)=2(33+14x)=66+28x`

Now, we have been told that the volume and the surface area are equal, so:

V = SA

`33x=66+28x`

Subtract `28x` from both sides:

`5x=66`

Divide both sides by 5:

`x=66/5= 13.2` inches