Help!! what value of r is the known surface area of a sphere, given by the function S(r)=4πr^2, numerically equal to the known volume of the sphere given by the function V(r)=4/3πr^3?

Question

can someone help me with these questions.

Write the equation of the square root function described.

The function value, f(x), is an ordered pair,(x,f(x) , on a circle of radius 5 with its center at the origin of a coordinate system. (Hint: The equation for a circle of radius r and its center at (0,0) x^2+y^2=r^2)

and

what value of r is the known surface area of a sphere, given by the function S(r)=4πr^2, numerically equal to the known volume of the sphere given by the function V(r)=4/3πr^3?

Answer 1

Set S(r) = V(r) and solve for r

Since

S(r) = 4πr²

and

V(r) = ⁴/₃πr³

Then

4πr² = ⁴/₃πr³

4πr² = ⁴/₃πr³

4 = ⁴/₃ r

Solve for r to get your answer