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Question
The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it ๐ = 3.14).
Solution
Let the ratio be x
Radius ‘r’ = 5x
Height ‘h’ = 12x
∴ Slant height `l` `=sqrt(r^2+h^2)=sqrt((5x)^2+(12x)^2)=13x`
Now volume = `2512cm^3`
⇒ `1/3xxpixx(5x)^2xx12x=2512`
⇒ `1/3xx3.14xx25x^2xx12x=2512`
⇒ `x^3=(2512xx3)/(314xx25xx2)`
⇒ x=2
∴ Slant height =` 13x=13xx2=26cm`
And, Radius of cone `=5x=5xx2=10cm`
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