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प्रश्न
The radii of the base of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?
उत्तर
Let r1 and r2 be the radii of the base of a cylinder and a cone.
The volume of cylinder`V_1 = pir_1^2 h_1`…… (i)
The volume of cone `V_2 = pir_2^2 h_2`…… (ii)
Dividing (i) by (ii), the, we get
`V_2/v_2 = (pir_1^2 h_1)/(1/3pir_2^2 h_2)`
`(= 3 xx (r_1/r_2)^2 xx (h_1/h_2))/(((r_1/r_2 = 3/4 , h_1 /h_2 = 2/3, "given")))`
`V_1/V_2= 3 xx (3/4)^2 xx 2/3`
`V_1/V_2 = 9/8`
`V_1 : V_2 = 9:8`
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