A solid cylinder of radius r and height h is placed over other cylinder of same height and radius.

Question

Write ‘True’ or ‘False’ and justify your answer:

A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is 4πrh + 4πr².

Answer 1

False

Explanation:

According to the question,

When one cylinder is placed over another, the base of first cylinder and top of other cylinder will not be covered in total surface area.

We know that,

Total surface area of cylinder = 2πrh + 2πr²h, where r = base radius and h = height

Total surface area of shape formed = 2(Total surface of single cylinder) – 2(Area of base of cylinder)

= 2(2πrh + 2πr²) – 2(πr²)

= 4πrh + 2πr²