Question

the volume of a sphere is the amount of space inside the sphere and is measured in cubic units. this could be calculated using the formula $v = \frac{4}{3}\pi r^{3}$, where $v$ represents the volume of the sphere, $r$ is the radius, and $\pi$ is a constant approximately equal to 3.14159.
a spherical satellite is used to collect atmospheric data. the satellite has a volume of approximately 5,000 cubic meters.
find the satellites radius using the formula for the volume of a sphere. use 3.14 for $\pi$ and round your answer to the nearest tenth.
use the keypad to enter the answer in the box.
the radius of the satellite is approximately
meters.

Explanation:

Step1: Substitute the values into the formula

Given \(V = 5000\) and \(\pi=3.14\), substitute into \(V=\frac{4}{3}\pi r^{3}\). So, \(5000=\frac{4}{3}\times3.14\times r^{3}\).

Step2: Solve for \(r^{3}\)

First, simplify the right - hand side: \(\frac{4}{3}\times3.14 = 4.1867\). Then the equation becomes \(5000 = 4.1867r^{3}\). Solving for \(r^{3}\), we get \(r^{3}=\frac{5000}{4.1867}\approx1194.2\).

Step3: Solve for \(r\)

Take the cube root of \(r^{3}\). \(r=\sqrt[3]{1194.2}\approx10.6\).

Answer:

\(10.6\)