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

Answer:

The volume is:

$V_{2}=9984\: ft^{3}$

Step-by-step 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.

$\frac{V_{1}}{V_{2}}=\frac{L*W*H}{L*W*13H}$

$\frac{768}{V_{2}}=\frac{L*W*H}{L*W*13H}$

L and W remain constant.

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

$\frac{768}{V_{2}}=\frac{1}{13}$

$V_{2}=13*768=9984\: ft^{3}$

I hope it helps you!