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


Also,


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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