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Question
If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then write the ratio of their weights.
Solution
The ratio of the volume of cones
`v_1 : v_2 = 1 : 4`
And `2r_1 :2r_2 = 4 : 5,`
i.e., `r_1 / r_2 = 4/5`
`"Now", v_1/v_2 = (1/3 pir_1^2 h_1)/(1/3 pir_2^2 h_2)`
`1/4 = (r_1/r_2)^2 xx (h_1/h_2)`
`h_1/h_2 = 1/4 xx 25 /16`
`= 25/ 64`
Hence, `h_1 : h_2 = 25 : 64`
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