Question

The approximate volume of the planet Mercury is cubic miles. To the nearest mile, what is the approximate radius of Mercury?The approximate radius of the planet Mercury is cubic miles.

Answer 1

From the statement, we know that the approximate volume of planet Mercury is:

$V=1.459\cdot10^{10}ml^3\text{.}$

The planet has a sphere shape. The volume of a sphere of radius r is:

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

Solving for the radius, we get:

$\begin{gathered} r^3=\frac{3}{4\pi}\cdot V, \\ r=\sqrt[3]{\frac{3}{4\pi}\cdot V}\text{.} \end{gathered}$

Replacing the value of V, we get:

$r=\sqrt[3]{\frac{3}{4\pi}\cdot1.459\cdot10^{10}ml^3}\cong1515.84767ml\cong1516ml.$

Answer

The radius of Mercury is approximately 1516 miles to the nearest mile.