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प्रश्न
Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?
उत्तर
Let the radius of the cone is 3x and x,
And the height of the cone is y and 3y.
Then,
Volume of the first cone
`v_1 = 1/3 pir^2 h`
`=1/3 pi (3x)^2 y`
`=1/3 pi9x^2 y`
` = 3pix^2 y ............(1)`
Volume of the second cone
`v_2 = 1/3 pi(x)^2 xx 3y`
=`pix^2 y` ............... (2)`
Then the radius of their volume
`v_1/v_2 = (3pi x^2 y)/(pi x^2 y)`
Or
`v_1/v_2 = 3:1`
`v_1 :v_2 = 3:1`
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