QuestionMoises's original volume is 37500 cm³. If shrunk by a scale factor of $k=\frac{1}{4}$ , what is his new volume?

Studdy Solution

STEP 1

Assumptions1. The original volume of Moises is $37500 \mathrm{~cm}^{3}$ . . The dilation scale factor is $k=\frac{1}{4}$ .
3. The volume dilation is cubed of the linear dilation factor.

STEP 2

We need to find the new volume of Moises after dilation. We can do this by multiplying the original volume by the cube of the scale factor.
$New\, volume = Original\, volume \\times (Scale\, factor)^{}$

STEP 3

Now, plug in the given values for the original volume and scale factor to calculate the new volume.
$New\, volume =37500 \mathrm{~cm}^{3} \\times \left(\frac{1}{}\right)^{3}$

STEP 4

Calculate the new volume.
$New\, volume =37500 \mathrm{~cm}^{3} \\times \left(\frac{1}{4}\right)^{3} =585.937 \mathrm{~cm}^{3}$ Zaire's new volume after being shrunk by the machine is $585.937 \mathrm{~cm}^{3}$ .

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