Question

what is the volume of this sphere? round your answer to the nearest hundredth. 12 yd cubic yards submit

Explanation:

Step1: Find the radius

The diameter \(d = 12\) yd. The radius \(r=\frac{d}{2}\), so \(r = \frac{12}{2}=6\) yd.

Step2: Use the volume formula for a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 6\) into the formula: \(V=\frac{4}{3}\pi(6)^{3}\).
First, calculate \((6)^{3}=6\times6\times6 = 216\). Then \(V=\frac{4}{3}\pi\times216\).
\(\frac{4}{3}\times216=4\times72 = 288\). So \(V = 288\pi\).
Take \(\pi\approx3.14159\), then \(V\approx288\times3.14159\).
\(288\times3.14159=(300 - 12)\times3.14159=300\times3.14159-12\times3.14159\).
\(300\times3.14159 = 942.477\), \(12\times3.14159=37.69908\).
\(V\approx942.477- 37.69908=904.77792\approx904.78\)

Answer:

\(904.78\)