Mensuration-19

A cardboard sheet in the form of a circular sector of radius 15 cm and
central angle 288⁰ is folded to make a cone. Find the volume of the cone.

Solution: Radius of the sector = 15 cm

Arc of the sector = 288/360 x 2 π R

= 288/360 x 2 x 22/7 x 15 cm

= 528/7 cm

The radius 15 cm becomes the slant height of the cone formed. If r is the radius of the base of cone,

then 2 π r = 528/7

r = 528/7 x 7/(2 x 22) = 12 cm

h = √( l² - r² )

= √(15² - 12²)

= √81 = 9

Therefore, h = 9 cm

Volume of the cone = 1/3 x π r² h

= 1/3 x 22/7 x 12 x 12 x 9 cu. cm

= 1357-5/7 cu. cm