Question

what is the volume of this sphere? round your answer to the nearest hundredth. 5 ft

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Identify the radius of the sphere

From the diagram, the radius \( r = 5\) ft.

Step3: Substitute the radius into the formula

Substitute \( r = 5\) into the formula: \( V=\frac{4}{3}\pi(5)^{3} \). First, calculate \( 5^{3}=125 \). Then, \( V=\frac{4}{3}\pi\times125=\frac{500}{3}\pi \).

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V=\frac{500}{3}\times3.14159\approx523.5983 \).

Step5: Round to the nearest hundredth

Rounding \( 523.5983 \) to the nearest hundredth gives \( 523.60 \).

Answer:

The volume of the sphere is approximately \( 523.60 \) cubic feet.