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प्रश्न
The ratio of radii of two cylinders is 1 : 2 and heights are in the ratio 2 : 3. The ratio of their volumes is ______.
विकल्प
1 : 6
1 : 9
1 : 3
2 : 9
उत्तर
The ratio of radii of two cylinders is 1 : 2 and heights are in the ratio 2 : 3. The ratio of their volumes is 1 : 6
Explanation:
Let r1, r2 be radii of two cylinders and h1, h2 be their heights.
Then `r_1/r_2 = 1/2` and `h_1/h_2 = 2/3`
Now, `V_1/V_2 = (pir_1^2 h_1)/(pir_2^2 h_2)`
= `(r_1/r_2)^2 xx h_1/h_2`
= `(1/2)^2 xx 2/3`
= `1/4 xx 2/3`
= `1/6`
= 1 : 6
Hence, V1 : V2 = 1 : 6
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