Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# 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. - Mathematics

Sum

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

Concept: Volume of Frustum of a Cone
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#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 7 Mensuration
Unit Exercise – 7 | Q 10 | Page 299