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A self-help group wants to manufacture joker’s caps (conical shapes) of 3 cm radius and 4 cm height. If the available colour paper sheet is then how many caps can be manufactured from that paper sheet?

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21 caps

22 caps

42 caps

15 caps

answer is A.

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Detailed Solution

It is given to us that the joker’s caps are conical in shape, with the base radius as 3 cm and the height as 4 cm.
The cone will look as follows:

https://www.vedantu.com/question-sets/1a287e14-d61e-445c-ac54-9df6b260e1a34493335839579131355.png

Thus, we can find the slant height with the help of Pythagoras theorem. Question Image

Hence, the slant height of the conical cap is 5 cm.
the curved surface area of a cone is given by the formula

Hence, the area of paper required for one cap is

The available area of sheet available with us

Therefore, we can find the number of caps as the quotient of the total sheet available with us and the area of sheet required for one cap.
Question Image

We have 21 caps that can be manufactured.
So, option 1 is correct.

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