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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