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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