Question

what is the volume of a sphere with a radius of 5.9 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Recall 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 of the sphere.

Step2: Substitute the given radius into the formula

Given that the radius \( r = 5.9 \) in. Substitute \( r = 5.9 \) into the formula:
\( V=\frac{4}{3}\pi(5.9)^{3} \)
First, calculate \( (5.9)^{3}=5.9\times5.9\times5.9 = 5.9\times34.81=205.379 \)
Then, \( \frac{4}{3}\pi\times205.379=\frac{4\times205.379\times\pi}{3}=\frac{821.516\pi}{3}\approx\frac{821.516\times3.14159}{3} \)
Calculate \( 821.516\times3.14159\approx821.516\times3 + 821.516\times0.14159\approx2464.548+116.32\approx2580.868 \)
Then, \( \frac{2580.868}{3}\approx860.289 \)

Step3: Round to the nearest tenth

The number \( 860.289 \) rounded to the nearest tenth is \( 860.3 \) (since the hundredth digit is 8, which is greater than or equal to 5, we round up the tenth digit).

Answer:

The volume of the sphere is approximately \( 860.3 \) cubic inches.