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 r_{s} = 25 cm

This r_{s} 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 r_{b} is the radius of the base of the cone

⇒ 2πr_{b} = 30π

⇒ r_{b} = 30cm

Also,

height of the cone = h

base radius = r_{b} = 15 cm

slant height = l = 25 cm

Applying Pythagoras theorem, we get:

h = √(l^{2} – r_{b}^{2})

= √(25^{2} – 15^{2})

= √(625 – 225) = √400 = 20 cm

= 1500π cm^{3}

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