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

# The volume of a cone is 100557 cu.cm. The area of its base is 20117 sq.cm. Find the slant height of the cone - Mathematics

Sum

The volume of a cone is 1005 5/7 cu.cm. The area of its base is 201 1/7 sq.cm. Find the slant height of the cone

#### Solution

Area of the base of a cone = 201 1/7 sq.cm

πr2 = 1408/7  ...(1)

Volume of a cone = 1005 5/7 cu.cm

1/3 pi"r"^2"h" = 7040/7

1/3 xx 1408/7 xx "h" = 7040/7  ...(from (1))

h = (7040 xx 3 xx 7)/(7 xx 1408)

= (7040 xx 3)/1408

= 5 × 3

= 15 cm

∴ Height of a cone = 15 cm

πr2 = 1408/7  ...(1)

22/7 xx "r"^2 = 1408/7

r2 = 1408/7 xx 7/22

r2 = 64

r = 8

Radius of a cone = 8 cm

Slant height of a cone (l) = sqrt("h"^2 + "r"^2)

= sqrt(15^2 + 8^2)

= sqrt(225 + 64)

= sqrt(289)

= 17 cm

∴ Slant height of a cone = 17 cm

Concept: Volume of Frustum of a Cone
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