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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