Question

The voleume of this sphere is 972pi cubic incher . what is the radious? the formula sphere V = 4/3 pi r3

Answer 1

V=4/3×π×r³

The volume is given, so we substitute it to the formula to get the equation and solve it for r.

$\displaystyle 972 \pi = \frac{4}{3} \pi r^3 \Rightarrow 972 \pi= \frac{4 \pi r^3}{3}$

$\displaystyle 4 \pi r^3 = 972 \pi \cdot 3 \Rightarrow 4 \pi r^3 = 2916 \pi$

$\displaystyle r^3 = \frac{2916 \pi}{4 \pi} \Rightarrow r^3=729 \Rightarrow r=\sqrt[3]{729}=9$

r = 9 in is your answer