Question

Suppose you have a sphere of radius r, and you also have a cylinder with radius r whose height is also r. The sum of the volumes of the sphere and the cylinder is

V=πr2⋅r+43πr3.

How can you rearrange the given equation to isolate r?

Answer 1

you almost have it already
v = πr^2*r + 4/3 πr^3
v = (1 + 4/3)πr^3
v = 7/3 πr^3
...

Answer 2

V = π r^2 + (4/3) π r^3
V = (3/3) π r^2 + (4/3)π r^3
V = (7 π / 3) (r^2 + r^3)
V / (7 π / 3) = (r^2 + r^3 )
r^3 + r^2 - 3 V / (7 π) = 0
solve cubic for r

Answer 3

Ignore what I said, had typo at start, left height out. Use what oobleck said.