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?

Answer 1

when we
$\pi{r}^{2}$
when we will find the area of earth and area of Pluto and dividing it we will get 30.112774413 as the answer.so we can take as 30 as the convenient answer.

Answer 2

Answer-

Approximately 275 spheres the size of Pluto will it take to have the same volume as Earth.

Solution-

We can calculate the number of spheres the size of Pluto will take to have the same volume as Earth, by dividing the volume of Earth by that of the Pluto.

We know that, volume of sphere is

$V=\frac{4}{3} \pi r^3$

Radius of Earth = 6,371 km, Radius of Pluto = 1,161 km

$V_{Earth}=\frac{4}{3} \pi (6,371)^3=1.08\times 10^{12}\\V_{Pluto}=\frac{4}{3} \pi (1,161)^3=6.56\times 10^9$

$\therefore \text{Number of spheres needed}=\frac{V_{Earth}}{V_{Pluto}} =\frac{1.08\times 10^{12}}{6.56\times 10^9} =274.39\approx 275$