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 cm3
= 2794.18 cm3
Volume of the cone = 2794.18 cm3
