The volume of a cylinder that fits exactly into a sphere is given by the formula:

V=\frac{1}{4}\pi h\left(4r^2-h^2\right)

where r is the radius of the sphere and h is the height of the cylinder.

What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?
Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: The volume of a cylinder that fits exactly into a sphere is given by the formula:

V=\frac{1}{4}\pi h\left(4r^2-h^2\right)

where r is the radius of the sphere and h is the height of the cylinder.

What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?
Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: The volume of a cylinder that fits exactly into a sphere is given by the formula:

V=\frac{1}{4}\pi h\left(4r^2-h^2\right)

where r is the radius of the sphere and h is the height of the cylinder.

What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?