Question

please answer with solution

find the radius of a sphere whose surface area and volume are numerically equal

Answer 1

formula for surface area of a sphere is \[SA = 4\pi r^2\]
the formula for volume is \[\frac 43 \pi r^3\]
if they are equal then \[4\pi r^2 = \frac 43 \pi r^3\]
if i divide both sides by \(4\pi\) i get \[\implies r^2 = \frac 13 r^3\]

i multiply both sides by 3
\[\implies 3r^2 = r^3\]
i subtract both sides by 3r^2
\[\implies r^3 - 3r^2 = 0\]
factor out r^2
\[\implies r^2 ( r - 3) = 0\]
solve for r now

does that help?