Question

A hollow cylinder of negligible thickness and radius r is mounted by a hollow sphere of same radius. The height of the cylinder is h. If the solid formed is to be painted. What is the total surface area that has to be painted?
A.$2\pi rh + 4\pi {r^2}$
B.$2\pi rh + \pi {r^2}$
C.$2\pi rh + 3\pi {r^2}$
D. None of the above

Answer 1

Hint: We are going to solve the given problem using formulae for finding the surface area cylinder and sphere.

Given that radius of hollow cylinder is r and height is h. and
Radius of the hollow sphere is also r.
The cylinder is mounted by the hollow sphere. We are painting the solid formed.
Total surface area painted = curved surface area of cylinder + curved surface area of sphere + area of base circle.
Let A be the total surface area formed.
$A = 2\pi rh + 2\pi {r^2} + \pi {r^2}$
$A = 2\pi rh + 3\pi {r^2}$

Note:
Surface area of any object is the area of an outer part of that object. It includes all faces of the object.