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Question
If the heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes?
Solution
Given that,
`h_1:h_2 = 1 : 2 " and " 2pir_1 :2pir_2 = 3 :4`
`i.e., r_1 :r_2 = 3:4`
Therefore,
The ratios of volume of their cones will be
`v_1 : v _2 = 1/3pi r_1^2 h_1 :1/3 pir_2^2 h_2`
`V_1/V_2 = (1/3 pir_1^2 h_1)/(1/3 pir_1^2 h_2)`
`=(r_1/r_2)^1 xx (h_1 /h_2)`
`V_1/V_2 = (3/4)^2 xx (1/2)`
`=9/32`
`V_1 :V_2 = 9: 32`
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