Question

question
what is the volume of a sphere with a radius of 49.5 in, rounded to the nearest tenth of a cubic inch?
answer attempt 1 out of 2
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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 \( r = 49.5 \) in. Then \( V=\frac{4}{3}\pi(49.5)^{3} \).
First, calculate \( (49.5)^{3}=49.5\times49.5\times49.5 = 121287.375 \).
Then \( V=\frac{4}{3}\pi\times121287.375 \).
\(\frac{4}{3}\times121287.375=161716.5\).
So \( V = 161716.5\pi \).

Step3: Calculate the numerical value

Using \( \pi\approx3.141592654 \), we have \( V\approx161716.5\times3.141592654\).
\(V\approx508018.6\) (rounded to the nearest tenth).

Answer:

\(508018.6\)