Question

Greetings my son needs help with this problem.A rectangular prism has a volume of 840 cubic inches. The height of the prism is 6 inches and the width is 10 inches. Find the length of the prism and explain how you found it.Can somebody help?

Answer 1

To find the volume of a rectangular prism, you have to multiply its length, width, and height following the formula:

`V=l*w*h`

If you know the volume, height, and width of the prism, you can use this formula to calculate the length.

- Write the formula in terms of the length (l), to do so you have to divide both sides by the product of w and h:

`\begin{gathered} V=l*w*h \\ (V)/(w*h)=(l*w*h)/(w*h) \\ (V)/(w*h)=\frac{l*\bcancel{w*h }}{\bcancel{w*h }} \\ (V)/(w*h)=l \end{gathered}`

The volume of the rectangular prism is V=840 in³, the height is h=6in, and the width is w=10in, use these values to find the length of the prism:

`\begin{gathered} l=(V)/(w*h) \\ l=(840)/(10*6) \\ l=(840)/(60) \\ l=14in \end{gathered}`

The length of the prism is 14 inches.