A cylinder and a cone have equal base radii and equal heights. If their curved surface areas are in the ratio 8 : 5, what is the ratio of their radii to heights ?
Question
A cylinder and a cone have equal base radii and equal heights. If their curved surface areas are in the ratio 8 : 5, what is the ratio of their radii to heights ?
Solution
The curved surface area of a cylinder is given by 2πrh, where r is the radius and h is the height. The curved surface area of a cone is given by πrl, where l is the slant height.
In this case, we are told that the cylinder and cone have equal base radii and equal heights. This means that the slant height of the cone is equal to the height of the cylinder.
Therefore, we can say that 2πrh (cylinder) is to πrh (cone) as 8 is to 5.
Solving this ratio for r/h gives us 8/5.
Therefore, the ratio of their radii to heights is 8:5.
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