Question : If the volume of two circular cones is in the ratio 4 : 1 and their diameter is in the ratio 5 : 4, then the ratio of their height is:
Option 1: 25 : 16
Option 2: 25 : 64
Option 3: 64 : 25
Option 4: 16 : 25
Correct Answer: 64 : 25
Solution : Given that the volume of the two cones is in the ratio 4 : 1. $⇒\frac{V_1}{V_2} = \frac {4} {1}$ Also, given that the diameter of the cones is in the ratio 5 : 4. $⇒\frac{d_1}{d_2}= \frac{5}{4}$ $⇒\frac{r_1}{r_2} =\frac{\frac{d_1}{2}}{\frac{d_2}{2}}= \frac{5}{4}$ where $r_1$ and $r_2$ denotes the radii of the two cones. Substituting these ratios into the formula, $⇒\frac{V_1}{V_2} = \frac{\frac{1}{3}\pi r_1^2h_1}{\frac{1}{3}\pi r_2^2h_2} = \frac{r_1^2h_1}{r_2^2h_2} $ $⇒\frac {4} {1}=(\frac{5}{4})^2×\frac{h_1}{h_2}$ $⇒\frac{h_1}{h_2}=\frac {64}{25} $ Hence, the correct answer is 64 : 25.
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Question : The volume of the two cones is in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. The ratio of their height is:
Option 1: 1 : 5
Option 2: 5 : 4
Option 3: 5 : 16
Option 4: 25 : 64
Question : The ratio of the curved surface area of two cones is 1 : 4 and the ratio of slant height of the two cones is 2 : 1. What is the ratio of the radius of the two cones?
Option 1: 1 : 2
Option 2: 1 : 4
Option 3: 1 : 8
Option 4: 1 : 1
Question : The heights of two right circular cones are in the ratio 1 : 5 and the perimeter of their bases are in the ratio 5 : 3. Find the ratio of their volumes.
Option 1: 8 : 11
Option 2: 7 : 6
Option 3: 5 : 9
Option 4: 3 : 4
Question : The ratio of curved surface areas of two cones is 1 : 8 and the ratio of their slant heights is 1 : 4. What is the ratio of radii of the two cones?
Option 1: 1 : 1
Option 2: 1 : 2
Option 3: 1 : 4
Option 4: 1 : 8
Question : The radii of two cylinders are in the ratio of 4 : 5 and their heights are in the ratio of 5 : 2. The ratio of their volume is:
Option 1: 9 : 4
Option 2: 2 : 1
Option 3: 9 : 7
Option 4: 8 : 5
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