Question

Please help 10 points

The height and width of a rectangular prism are each 2 inches shorter than the length of the prism. The volume of the prism is 40 cubic inches. Approximate the dimensions of the prism to the nearest hundredth. Show work.

Answer 1

The length of the prism is 4.87 inches

The width of the prism is 2.87 inches

The height of the prism is 2.87 inches

Explanation:

Let

l -----> the length of the prism in inches

w ----> the width of the prism in inches

h---> the height of the prism in inches

we know that

The volume of the prism is

`V=lwh`

we have

`V=40\ in^3`

so

`40=lwh` -----> equation A

`w=l-2` ----> equation B

`h=l-2` -----> equation C

substitute equation B and equation C in equation A and solve for l

`40=l(l-2)(l-2)\\\\40=l(l^(2)-4l+4)\\\\40=l^(3)-4l^(2)+4l\\\\l^(3)-4l^(2)+4l-40=0`

Solve the cubic equation by graphing

using a graphing tool

The solution is l=4.87 in

see the attached figure

Find the value of w

`w=4.87-2=2.87\ in`

`h=4.87-2=2.87\ in`

The approximate dimensions of the prism are

The length of the prism is 4.87 inches

The width of the prism is 2.87 inches

The height of the prism is 2.87 inches