Question

A sphere is inscribed in a cylinder. The surface area of the sphere and the lateral area of the cylinder are equal.

true?

Answer 1

let r = radius of cylinder
when you draw a sphere that fits exactly inside a cylinder, you will observe that
radius of cylinder = radius of sphere, and
height of cylinder = diameter of sphere

recall that
surface area of sphere = 4*pi*r^2
and
lateral surface area of cylinder = 2*pi*r*h
since h = diameter of sphere = 2r
2*pi*r*(2r)
4*pi*r^2

thus, it's TRUE.

hope this helps~ :)