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प्रश्न
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
विकल्प
1 : 4
1 : 3
3 : 1
2 : 5
उत्तर
Let V1 and V2 be the volume of the two cylinders with radius r1 and height h1, and radius r2and height h2, where `(2r_1)/(2r_2) = 3/1,h_1/h_2 = 1/3`
So,
`V_1 = pir_1^2h_1` ……. (1)
Now,
`V_2 = pir_2^2h_2` …… (2)
From equation (1) and (2), we have
`V_1/V_2 = (r_1/r_2)^2(h_1/h_2)`
`⇒ V_1/V_2 = ((2r_1)/(2r_2))^2 (h_1/h_2)`
`⇒V_1/V_2 = (3)^2(1/3)=3/1`
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