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Q.

A child wants to make caps for everyone on his birthday. He has a single cap and wants to make 10 more for his friends. If the cap is in the form of a right circular cone with base radius 7 cm and height 24 cm, the area of the sheet required to make 10 such caps will be ____ c m 2 .  


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Detailed Solution

A child wants to make caps for everyone on his birthday. He has a single cap and wants to make 10 more for his friends. If the cap is in the form of a right circular cone with base radius 7 cm and height 24 cm, the area of the sheet required to make 10 such caps will be 5500  cm 2 .  
We are given a cap in the form of a right circular cone, with base radius 7 cm and height 24 cm.
We know that the area of a cone is πrl,   where r is the radius and l is the slant height of the cone.
Since radius and height of the given cap are 7 cm and 24 cm respectively, we can calculate slant height as,
     l 2 = r 2 + h 2 l 2 = 7 2 + 24 2 l 2 =49+576 l 2 =625  
l= 625 l=25cm  
The area of the sheet required for making 1 cap will be,
A=πrl = 22 7 ×7×25 =550 cm 2   Therefore area of the sheet required for 10 caps will be, 550×10=5500 cm 2 .  
 
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