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Question
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
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