Question

The volume of a rectangular prism is 768 ft3. What is the volume of the same shape if the width is changed by a scale factor of 13?

Answer 1

The volume is:

`V_(2)=9984\: ft^(3)`

Explanation:

The equation of the volume of a rectangular prism is:

`V=L*W*H`

Where:

• L is the length
• W is the width
• H is the height

We know the volume is 768 ft³ and the new width change a 13 factor, in other words, W(2) = 13W(1), so we can divide each equation of the volume to find the new volume.

`(V_(1))/(V_(2))=(L*W*H)/(L*W*13H)`

`(768)/(V_(2))=(L*W*H)/(L*W*13H)`

L and W remain constant.

Therefore, we just need to solve it for V(2).

`(768)/(V_(2))=(1)/(13)`

`V_(2)=13*768=9984\: ft^(3)`

I hope it helps you!