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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?

Sagot :

whitneytr12

Answer:

The volume is:

[tex]V_{2}=9984\: ft^{3}[/tex]

Step-by-step explanation:

The equation of the volume of a rectangular prism is:

[tex]V=L*W*H[/tex]

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.

[tex]\frac{V_{1}}{V_{2}}=\frac{L*W*H}{L*W*13H}[/tex]

[tex]\frac{768}{V_{2}}=\frac{L*W*H}{L*W*13H}[/tex]

L and W remain constant.

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

[tex]\frac{768}{V_{2}}=\frac{1}{13}[/tex]

[tex]V_{2}=13*768=9984\: ft^{3}[/tex]

I hope it helps you!

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