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A cone, a hemisphere and a cylinder stand on equal bases of radius R and have equal heights H. Their whole surface are in the ratio:

A (√3+1): 3:4
B (√2+1): 7:8
C (√2+1): 3:4
D None of these

User PerduGames
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1 Answer

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Final answer:

The question involves calculating the surface areas of a cone, a hemisphere, and a cylinder to determine their ratio. The areas are found using geometric formulas and the given equality of their bases and heights.

Step-by-step explanation:

The question asks for the ratio of the whole surface areas between three geometric shapes: a cone, a hemisphere, and a cylinder.

All shapes stand on equal bases with radius R and have equal heights H. To find the ratios, we must calculate the surface area for each shape and compare them.

For a cone, the lateral surface area is πRl (where l is the slant height) and the base area is πR^2. For a hemisphere, the surface area (including the base) is 3πR^2. Lastly, for a cylinder, the surface area is 2πRH (lateral) plus 2πR^2 (top and bottom bases).

To make further deductions, we need to use the given relations, R and H are equal among the shapes, and consider the slant height l of the cone which can be found through the Pythagorean theorem (l = √(R^2 + H^2)).

From this information, we can calculate and compare the total surface areas to find the ratio sought in the question.

User Brian Schmitt
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