# Question from mensuration. A piece of paper is in the shape of a sector of a circle whose radius is 12cm and the central angle of the sector is 120 degree it is rolled to form a cone of the biggest possible capacity .Find the capacity of the cone.

1
by Rahamathulla

## Answers

2014-11-09T01:42:57+05:30

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Lateral or slanting height of cone L
= radius of the circle from which the sector is cut
L   = 12 cm

Arc length of the 120° sector = 2π * radius * 120°/360° = 8 π cm

Circumference of the base circle of cone = arc length = 8π cm = 2 π R
So,   R  = radius of the circle of base of cone = 4 cm

Area of base of cone = πR² = 16 π cm²

Altitude or Height of cone = H = √(L² - R²) = √(12² - 4²) = √128 = 8√2 cm

Volume or capacity of Cone  =  1/3 * base area *  Altitude
= 1/3 * 16 π * 8 √2 = 128√2π / 3 cm³

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