# Mensuration-19

### From Homeworkwiki

**A cardboard sheet in the form of a circular sector of radius 15 cm and central angle 288 ^{0} 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 = √( l^{2} - r^{2} )

= √(15^{2} - 12^{2})

= √81 = 9

Therefore, h = 9 cm

Volume of the cone = 1/3 x π r^{2} h

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

= 1357-5/7 cu. cm