Question : The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. The ratio of their volumes is equal to:
Option 1: 9 : 10
Option 2: 8 : 9
Option 3: 9 : 11
Option 4: 7 : 10
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Correct Answer: 9 : 10
Solution : Given: The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. Let the radii of two cylinders be $3x$ and $4x$ and their heights be $8y$ and $5y$. Use the formulas, The volume of the cylinder = $\pi r^2h$, where $r$ and $h$ are the radius and height respectively. The ratio of their volumes = $\frac{\pi\times (3x)^2\times 8y}{\pi\times (4x)^2\times 5y}=\frac{9\times8}{16\times 5}=\frac{9}{10}$. Hence, the correct answer is 9 : 10.
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Question : The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is _______.
Option 1: 27 : 20
Option 2: 20 : 27
Option 3: 4 : 9
Option 4: 9 : 4
Question : The radii of two cylinders are in the ratio 1 : 4 and their heights are in the ratio 4 : 3. Their volumes will be in the ratio ______.
Option 1: 1 : 12
Option 2: 2 : 9
Option 3: 3 : 10
Option 4: 1 : 9
Question : The ratio of the radii of the two cones is 5 : 6 and their volumes are in the ratio of 8 : 9. The ratio of their heights is:
Option 1: 32 : 25
Option 2: 25 : 32
Option 3: 27 : 20
Option 4: 20 : 27
Question : The area of the two triangles is in the ratio 5 : 3 and their heights are in the ratio 5 : 7. Find the ratio of their bases.
Option 1: 3 : 5
Option 2: 7 : 3
Option 3: 7 : 5
Option 4: 2 : 3
Question : A cone and a cylinder with equal radii have equal volumes. The ratio of their heights is:
Option 1: 2 : 3
Option 2: 3 : 4
Option 3: 1 : 2
Option 4: 3 : 1
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