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Question
Two right circular cone x and y are made x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y.
Solution
Let radius of cone y = r
Therefore, radius of cone x = 3r
Let volume of cone y = V
Then volume of cone x = 2V
Let h1 be the height of x and h2 be the height of y.
Therefore, Volume of cone =`1/3pir^2h`
Volume of cone `x = 1/3pi(3r)^2h_1`
= `1/3pi9r^2h_1`
= `3pir^2h_1`
Volume of cone `y = 1/3pir^2h_2`
∴ `(2V)/v = (3pir^2h_1)/(1/3pir^2h_2)`
`=> 2/1 = (3h_1 xx 3)/h_2 = (9h_1)/h_2`
`=> h_1/h_2 = 2/1 xx 1/9 = 2/9`
∴ h1 : h2 = 2 : 9
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