Question

what is the volume of a sphere with a radius of 6 mm? sphere $v = \frac{4}{3} \pi r^{3}$ $v = 288\pi mm^{3}$ $v = 648\pi mm^{3}$ $v = 512\pi mm^{3}$ $v = 216\pi mm^{3}$

Explanation:

Step1: Substitute the radius into the formula

Given \( r = 6\) mm and the formula \( V=\frac{4}{3}\pi r^{3}\), substitute \( r = 6\) into the formula: \( V=\frac{4}{3}\pi\times(6)^{3}\).

Step2: Calculate \(6^{3}\)

\(6^{3}=6\times6\times6 = 216\). So the formula becomes \( V=\frac{4}{3}\pi\times216\).

Step3: Simplify the expression

\(\frac{4}{3}\times216=\frac{4\times216}{3}=4\times72 = 288\). So \( V = 288\pi\) mm³.

Answer:

\(V = 288\pi\) mm³