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Question
Two-cylinder have bases of the same size. The diameter of each is 14 cm. One of the cones is 10 cm high and the other is 20 cm high. Find the ratio between their volumes.
Solution
| Cone I | Cone II | |
| Base diameter | 14 cm | 14 cm |
| Base radius | r1 = 7 cm | r2 = 7 cm |
| Height | h1 = 10 cm | h2 = 20 cm |
| Volume | V1 = π r12h1 | V2 = πr22h2 |
Volume = V1 = π r12h1 : V2= πr22h2
Volume = π x (7)2 x 10 cm3 : π x (7)2 x 20 cm3
Volume = 490 π cm3 : 980 π cm3
∴ `V_1/V_2 = (490 π)/(980 π) = 1/2`
∴ V1 : V2 = 1 : 2.
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