you almost have it already
v = πr^2*r + 4/3 πr^3
v = (1 + 4/3)πr^3
v = 7/3 πr^3
...
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?
3 answers
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
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
Ignore what I said, had typo at start, left height out. Use what oobleck said.