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Question
The radius and the height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone. (Take π = 3.14)
Solution
The ratio between radius and height = 5 : 12
Volume = 2512 cubic cm
Let radius (r) = 5x, height (h) = 12x and slant height = l
l2 = r2 + h2
`=>` l2 = (5x)2 + (12x)2
`=>` l2 = 25x2 + 144x2
`=>` l2 = 169x2
`=>` l = 13x
Now volume = `1/3pir^2h`
`=> 1/3pir^2h = 2512`
`=> 1/3(3.14)(5x)^2(12x) = 2512`
`=> 1/3(3.14)(300x^3) = 2512`
∴ `x^3 = (2512 xx 3)/(3.14 xx 300)`
= `(2512 xx 3 xx 100)/(314 xx 300)`
= 8
`=>` x = 2
∴ Radius = 5x = 5 × 2 = 10
Height = 12x = 12 × 2 = 24 cm
Slant height = 13x = 13 × 2 = 26 cm
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