The given figure shows a solid whose bottom part is a cylinder and top part is a hemisphere. What is the ratio of the curved surface areas of the bottom part and the top part?
Question
The given figure shows a solid whose bottom part is a cylinder and top part is a hemisphere. What is the ratio of the curved surface areas of the bottom part and the top part?
Solution
To find the ratio of the curved surface areas of the bottom part and the top part, we need to calculate the curved surface areas of both the cylinder and the hemisphere separately.
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Curved Surface Area of the Cylinder: The curved surface area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height of the cylinder. In this case, the bottom part of the solid is a cylinder. Let's assume the radius of the cylinder is r1 and the height is h1.
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Curved Surface Area of the Hemisphere: The curved surface area of a hemisphere is given by the formula 2πr^2, where r is the radius of the hemisphere. In this case, the top part of the solid is a hemisphere. Let's assume the radius of the hemisphere is r2.
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Calculate the Curved Surface Areas: Using the given information, calculate the curved surface areas of both the cylinder and the hemisphere.
Curved Surface Area of the Cylinder = 2πr1h1 Curved Surface Area of the Hemisphere = 2πr2^2
- Find the Ratio: Finally, divide the curved surface area of the bottom part (cylinder) by the curved surface area of the top part (hemisphere) to find the ratio.
Ratio = (Curved Surface Area of the Cylinder) / (Curved Surface Area of the Hemisphere)
By following these steps, you can find the ratio of the curved surface areas of the bottom part and the top part of the given solid.
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