From a solid cylinder whose height is 24 cm  and diameter 20 cm  , a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

# From a solid cylinder whose height is  and diameter  , a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

1. A
2600 cm2
2. B
2640 cm2
3. C
2145 cm2
4. D
2500 cm2

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### Solution:

Given that from a solid cylinder having diameter 20 cm and height 24 cm, a conical cavity of same diameter and height is hollowed out.
The curved surface area of a cylinder of radius, r and height, h is given by  .
The curved surface area of a cone of radius, r, slant height, l and height, h is given by   where  .
Radius of conical cavity is  .
The height of cone is 24 cm.
Therefore,

The slant height of the cone is 26 cm.
The curved surface area of cylinder =  .
⇒ CSA of cylinder   ⇒ CSA of cylinder     The curved surface area of cone =  .
⇒ CSA of cone   ⇒ CSA of cone
The area of upper circular base of cylinder by =  .
⇒ Area   ⇒Area   The total surface area of remaining solid = CSA of cylinder + CSA of cone + Area of circular base.

⇒ TSA
⇒ TSA
⇒ TSA =
Hence, the total surface area of remaining solid is 2640 cm  .
Therefore, the correct answer is option (2).

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