Question

The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as Earth?
A.
121
B.
154
C.
165
D.
176
E.
189

Answer 1

volume of sphere = (4/3) pi *r^3

"Approximately how many spheres the size of Pluto does it take to have the same volume as Earth?" ----> divide (volume of Earth) / (volume of Pluto)

*however* you don't actually need to calculate the volume of both planets.

I'll demonstrate why.

let's let r = radius of Pluto and R = radius of Earth

Volume of Earth = (4/3) pi *R^3
Volume of Pluto = (4/3) pi *r^3

notice how, when you divide earth's volume/ pluto's volume, all the 4/3 and pi cancels out and you're left with R^3 / r^3