Question

lianne drew a sphere with a radius of 7 in. she calculated its volume as follows.
\\( \frac { 2 } { 3 } \pi \mathrm { in } ^ { 3 } \\)
what value should be multiplied by \\( \pi \\) in the numerator to correctly show the volume of the sphere?

Explanation:

Step1: Recall the formula for the volume of a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\).

Step2: Substitute the radius \(r = 7\) into the formula

Substitute \(r = 7\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi\times7^{3}\).
Calculate \(7^{3}=7\times7\times7 = 343\). Then \(V=\frac{4\times343}{3}\pi=\frac{1372}{3}\pi\).

Answer:

\(1372\)