Question : If the ratio of areas of two circles is 4 : 9, then the ratio of their circumferences will be:
Option 1: 3 : 2
Option 2: 9 : 4
Option 3: 2 : 3
Option 4: 4 : 9
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Correct Answer: 2 : 3
Solution : The area of the two circles is in the ratio of 4 : 9. Let their radii be $r_1$ and $r_2$, respectively. So, $\pi r_{1}^{2}:\pi r_{2}^{2}$ = 4 : 9 $⇒\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{4}{9}$ $⇒\frac{r_{1}}{r_{2}} = \frac{2}{3}$ $\therefore$ Circumference = $2\pi r_{1}:2\pi r_{2} = \frac{2 \pi \times 2}{2 \pi \times 3}$ = 2 : 3 Hence, the correct answer is 2 : 3.
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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 : 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 : 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 : 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 3: 5 : 7
Option 4: 9 : 5
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
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