Q. 35.0( 1 Vote )

A sector of central angle 216° is cut out from a circle of radius 25 centimetres and is rolled up into a cone. What are the base radius and height of the cone? What is its volume?

Answer :

Given that radius of the circle is 25 cm.

This will be same as the radius of the sector rs = 25 cm

This rs will be the slant height of the cone

Slant height = 25 cm

Central angle θ = 216°

The length of arc will be

Thus, the length of arc will be .

But this is same as the circumference of the base of the cone

So if rb is the radius of the base of the cone

2πrb = 30π

rb = 30cm


height of the cone = h

base radius = rb = 15 cm

slant height = l = 25 cm

Applying Pythagoras theorem, we get:

h = √(l2 – rb2)

= √(252 – 152)

= √(625 – 225) = √400 = 20 cm

= 1500π cm3

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