A right circular cylinder is inscribed in a sphere of radius $r = 5 \mathrm {~cm}$. Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.
A) $157.08 \mathrm {~cm} ^ { 2 }$
B) $177.08 \mathrm {~cm} ^ { 2 }$
C) $187.08 \mathrm {~cm} ^ { 2 }$
D) $167.08 \mathrm {~cm} ^ { 2 }$
E) $197.08 \mathrm {~cm} ^ { 2 }$

Question

Quizplus · Accepted Answer

The largest possible surface area of the cylinder occurs when its height is equal to its diameter, which is equal to the diameter of the sphere. Thus, the height and radius of the cylinder are both $5 \mathrm {~cm}$. The surface area of the cylinder is given by $2\pi r h + 2\pi r^2 = 2\pi (5)(5) + 2\pi (5)^2 = 100\pi + 50\pi = 150\pi \approx 157.08 \mathrm {~cm} ^ { 2 }$.

A Right Circular Cylinder Is Inscribed in a Sphere of Radius