Question

A cylinder of radius r is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is

Options

• 2πr(r + 13)

• 13πr

• 2π(13 + r)²

• 26πr

Answer 1

26πr

Explanation:

Given:

Radius of cylinder and hemisphere = r

Total height of the object = 13 cm

Since the hemisphere is surmounted on the cylinder, total height = height of cylinder + radius of hemisphere

Let height of cylinder = h

So, h + r = 13

⇒ h = 13 – r

We need to find the inner surface area of the object.

Inner surface area includes:

Curved surface area of the cylinder = 2πrh

Inner curved surface area of the hemisphere = 2πr² (since surface area of a full sphere is 4πr², hemisphere is half of it)

Total inner surface area = 2πrh + 2πr²

= 2πr(h + r)

Substitute h = 13 – r:

2πr(13 – r + r) = 2πr(13)

= 26πr