Question

a large sand dune in the desert is shaped like a sphere. the dune has a volume of approximately 65,000 cubic meters. find the radius of the sand dune using the formula for the volume of a sphere. use 3.14 for π and round your answer to the nearest tenth.
use the keypad to type your answer in the box provided.
the radius of the sand dune is approximately □ meters.

Explanation:

Step1: Write the formula for the volume of a sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\), where \(V\) is the volume and \(r\) is the radius.

Step2: Substitute the given values into the formula

We know that \(V = 65000\) cubic meters and \(\pi=3.14\). So, \(65000=\frac{4}{3}\times3.14\times r^{3}\).
First, simplify \(\frac{4}{3}\times3.14=\frac{12.56}{3}\approx4.19\). Then the equation becomes \(65000 = 4.19r^{3}\).

Step3: Solve for \(r^{3}\)

Divide both sides of the equation \(65000 = 4.19r^{3}\) by \(4.19\). So, \(r^{3}=\frac{65000}{4.19}\approx15513.13\).

Step4: Solve for \(r\)

Take the cube - root of both sides. \(r=\sqrt[3]{15513.13}\). Using a calculator, \(r\approx24.9\) (rounded to the nearest tenth).

Answer:

\(24.9\)