Question : If the ratio of the volumes of two cylinders is 6 : 5 and the ratio of their heights is 5 : 24, then what is the ratio of their radii?
Option 1: 12 : 7
Option 2: 5 : 6
Option 3: 1 : 2
Option 4: 12 : 5
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Correct Answer: 12 : 5
Solution : Given: the ratio of the volumes of two cylinders is 6 : 5 and the ratio of their heights is 5 : 24. Let their radii be $r_1$ and $r_2$, also let their heights be $5h$ and $24h$. According to the question, $\frac{\pi×r_1^2×5h}{\pi×r_2^2×24h}=\frac{6}{5}$ ⇒ $\frac{r_1^2}{r_2^2}=\frac{144}{25}$ ⇒ $\frac{r_1}{r_2}=\frac{12}{5}$ $\therefore r_1:r_2=12:5$ Hence, the correct answer is 12 : 5.
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Question : If the ratio of the volumes of two cylinders is 7 : 5 and the ratio of their heights is 5 : 7, then what is the ratio of their radii?
Option 1: 5 : 7
Option 2: 3 : 4
Option 3: 5 : 9
Option 4: 4 : 5
Question : If the heights of two cylinders are in the ratio of 7 : 9 and their diameters are in the ratio of 6 : 7, then what is the ratio of the volumes of the cylinders?
Option 1: 6 : 7
Option 2: 7 : 9
Option 4: 4 : 7
Question : Two cylinders have their heights in the ratio 1 : 2 and their radii in the ratio 2 : 1. What is the ratio of their volumes?
Option 1: 3 : 1
Option 2: 1 : 3
Option 3: 2 : 1
Option 4: 1 : 2
Question : The ratio of radii of a cylinder to a cone is 3 : 1. If their heights are equal, What is the ratio of their volumes?
Option 1: 1 : 3
Option 2: 27 : 1
Option 3: 9 : 1
Option 4: 1 : 9
Question : The lengths, the breadths, and the volumes of two cuboids are in the ratios of 4 : 5, 3 : 4, and 2 : 3, respectively. What is the ratio of their heights?
Option 1: 3 : 5
Option 2: 10 : 9
Option 3: 8 : 15
Option 4: 2 : 3
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