Question

what is the volume of a sphere with a diameter of 9.6 m, rounded to the nearest tenth of a cubic meter?

Explanation:

Step1: Find the radius

The diameter \( d = 9.6 \) m, so the radius \( r=\frac{d}{2}=\frac{9.6}{2} = 4.8 \) m.

Step2: Use the sphere volume formula

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \). Substitute \( r = 4.8 \) into the formula:
\( V=\frac{4}{3}\pi(4.8)^{3} \)
First, calculate \( (4.8)^{3}=4.8\times4.8\times4.8 = 110.592 \)
Then, \( \frac{4}{3}\times110.592 = 147.456 \)
So, \( V = 147.456\pi \)
Calculate the numerical value: \( 147.456\times3.14159\approx463.0 \) (rounded to the nearest tenth)

Answer:

The volume of the sphere is approximately \( 463.0 \) cubic meters.