Question

Suppose the volume of a rectangular shopping cart basket is 12,090 cubic inches. If the length measures 31 inches and the width measures 19.5 inches, how high is the shopping cart basket?

Answer 1

`\boxed {\tt h=20\ inches}`

Explanation:

The volume of a rectangular prism can be found using the following formula.

`v=l*w*h`

We know that the volume is 12,090 cubic inches, the length is 31 inches, and the width is 19.5 inches.

`v= 12,090 \ in^3\\l=31 \ in \\ w=19.5 \ in`

`12,090 \ in^3= 31 \ in * 19.5 \ in * h`

Multiply 31 inches and 19.5 inches.

`12,090 \ in^3= 604.5 \ in^2 * h`

We are trying to find h, therefore we must isolate it. h is being multiplied by 604.5 square inches. The inverse of multiplication is division. Divide both sides of the equation by 604.5 in²

`(12,090 \ in^3)/(604.5 \ in^2)= (604.5 \ in^2 *h)/(604.5 \ in^2)`

`(12,090 \ in^3)/(604.5 \ in^2)=h`

`20 \ in =h`

The height of the shopping basket is 20 inches.