Question

what is the volume of this sphere?
round your answer to the nearest hundredth.
34.4 in
cubic inches
submit

Explanation:

Step1: Find the radius

The diameter \(d = 34.4\) inches. The radius \(r=\frac{d}{2}\).
\(r=\frac{34.4}{2}=17.2\) inches.

Step2: Use the volume formula for a sphere

The volume formula for a sphere is \(V = \frac{4}{3}\pi r^{3}\).
Substitute \(r = 17.2\) into the formula:
\(V=\frac{4}{3}\pi(17.2)^{3}\).
First, calculate \((17.2)^{3}=17.2\times17.2\times17.2 = 5088.448\).
Then, \(V=\frac{4}{3}\pi\times5088.448\).
\(V=\frac{20353.792}{3}\pi\).
Take \(\pi\approx3.14159\).
\(V=\frac{20353.792\times3.14159}{3}\).
\(20353.792\times3.14159 = 20353.792\times(3 + 0.14159)=20353.792\times3+20353.792\times0.14159=61061.376+2883.297\approx63944.673\).
\(V=\frac{63944.673}{3}\approx21314.89\)

Answer:

\(21314.89\)