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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?

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Answer:

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!

User Arzar
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