A metallic sheet in the form of a sector of a circle of radius 21 cm has a central angle of 216°. The sector is made into a cone by bringing the bounding radii together. Find the volume of the cone formed.

#### Solution

Radius of a cone (r) = 21 cm

Central angle (θ) = 216°

Let “R” be the radius of a cone

Circumference of the base of a cone = arc length of the sector

2πR = `theta/360 xx 2pi"r"`

R = `theta/360 xx "r"`

R = `216/360 xx 21 "cm"`

= 12.6 cm

Slant height of a cone (l) = 21 cm

h = `sqrt("l"^2 - "r"^2)`

= `sqrt(21^2 - 12.6^2)`

= `sqrt((21 + 12.6)(21 - 12.6))`

= `sqrt((33.6)(8.4))`

= `sqrt((336 xx 84)/100)`

= `sqrt(28224)`

h = `168/10`

= 16.8 cm

Volume of the cone = `1/3 pi"R"^2"h"` cu.units

= `1/3 xx 22/7 xx 12.6 xx 12.6 xx 16.8 "cm"^3`

= 22 × 4.2 × 1.8 × 16.8 cm^{3}

= 2794.18 cm^{3}

Volume of the cone = 2794.18 cm^{3}