Question

a spherical weather balloon is used to measure atmospheric conditions. the balloon has a volume of approximately 75,000 cubic meters.
find the radius of the balloon 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 enter the answer in the box.
the radius of the weather balloon is approximately meters.

Explanation:

Step1: Write the formula for the volume of a sphere

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

Step2: Substitute the given values into the formula

We know that \( V = 75000\) and \( \pi=3.14\). So, \( 75000=\frac{4}{3}\times3.14\times r^{3}\).
First, simplify the right - hand side: \(\frac{4}{3}\times3.14 = 4.1867\) (approx). Then the equation becomes \(75000 = 4.1867r^{3}\).

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

Divide both sides of the equation by \(4.1867\): \(r^{3}=\frac{75000}{4.1867}\approx17914.7\).

Step4: Solve for \( r\)

Take the cube root of both sides: \(r=\sqrt[3]{17914.7}\). Using a calculator, \(r\approx26.2\).

Answer:

\(26.2\)