Question : If the surface area of two spheres is in the ratio 81 : 25, then what is the ratio of their radius?
Option 1: 5 : 8
Option 2: 7 : 9
Option 3: 5 : 7
Option 4: 9 : 5
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Correct Answer: 9 : 5
Solution : Let the radii of two spheres be $r, R$, respectively. According to the question, $\frac{4\pi r^2}{3\pi R^2}=\frac{81}{25}$ $⇒\frac{r^2}{R^2}=\frac{81}{25}$ $\therefore \frac{r}{R}=\frac{9}{5}$ Hence, the correct answer is 9 : 5.
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Question : The radius of two spheres is in the ratio of 1 : 5. What is the ratio of the volume of the two spheres?
Option 1: 8 : 27
Option 2: 1 : 25
Option 3: 1 : 125
Option 4: 1 : 64
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 : The surface areas of the two spheres are in the ratio of 64 : 81. Find the ratio of their volumes, in the order given.
Option 1: 512 : 729
Option 2: 64 : 729
Option 3: 8 : 81
Option 4: 4 : 9
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 4: 4 : 7
Question : The ratio of the total surface areas of the two cubes is 49 : 81. What is the ratio of their volumes?
Option 1: 343 : 729
Option 2: 294 : 486
Option 3: 7 : 9
Option 4: 49 : 121
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