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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

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#### Solution

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

πr^{2} = `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

πr^{2} = `1408/7` ...(1)

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

r^{2} = `1408/7 xx 7/22`

r^{2} = 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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