Question

an artist is asked to scale up a model of pluto to 3 times its original size. if the original model of pluto has a radius of 12 cm, what is the volume of the new model? the volume of the new model of pluto is 195,432.20 cm³. the volume of the new model of pluto is 21,714.69 cm³. the volume of the new model of pluto is 268.08 cm³. the volume of the new model of pluto is 7,238.23 cm³.

Explanation:

Step1: Find the new radius

The original radius is 12 cm and it is scaled up 3 - times. So the new radius $r = 12\times3=36$ cm.

Step2: Use the volume - formula for a sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 36$ cm into the formula.
$V=\frac{4}{3}\times\pi\times(36)^{3}$
$V=\frac{4}{3}\times\pi\times46656$
$V = 4\times\pi\times15552$
$V=62208\pi\approx62208\times3.14 = 195432.12\approx195432.20$ $cm^{3}$

Answer:

The volume of the new model of Pluto is 195,432.20 $cm^{3}$.