Q. 24.3( 4 Votes )
What is the central angle of the sector to be used to make a cone of base radius 10 centimetres and slant height 25 centimetres?
Answer :
Given that slant height of the cone should be 25 cm.
So radius of the sector rs = 25 cm
To find: Central angle θ
Radius of the base rb = 10 cm
So circumference of the base = 2πrb = 2π×10 = 20π cm ..(1)
This circumference is equal to the length of the arc
The length of arc will be 
Thus, the length of arc will be 
. …(2)
Equating the results in (1) and (2):
⇒ θ = 144°
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