Question

Find the dimensions of a rectangularprism with a volume of 512 cubic cm ifthe width is one-half the length and theheight is four times the width.

Answer 1

Feel free to let me know how I did by rating our session once you close itThe volume of a rectangular prism

The volume of a rectangular prism of base width W, base length L, and height H is:

V = W.L.H

We are given the width is one-half the length, i.e.:

W=1/2L

We also know the height is 4 times the width, thus:

H=4W

Using the previous relation:

H=4(1/2L)=2L

Now we have all dimensions in terms of L. substitute in the formula of the volume:

V = (1/2L).L.(2L)

Multiplying:

`V=L^3`

Since the volume is given as V=512 cubic cm:

`\begin{gathered} L^3=512 \\ \text{Solving:} \\ L=\sqrt[3]{512}=8 \end{gathered}`

The length is 8 cm, now find the width:

W=1/2L=1/2*8 = 4 cm

Finally, the height is:

H=4W=4*4 = 16 cm.

The dimensions of the prism are: Length=8 cm, Width=4 cm, Height= 16 cm