Q3 of 35 Page 202

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?

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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