A right circular cylinder just encloses a sphere of radius r as shown in the figure. What is the ratio of the surface area of the sphere to the surface area of the cylinder?

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1:1

1:2

1:4

1:3

answer is A.

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Detailed Solution

Given, the radius of the sphere = r units.
Question Image

The radius of the cylinder will also be r units.
Since the cylinder is big enough to fit in the sphere, its height will be 2r.
The surface area of the sphere will be

4 π r 2

.
The curved surface area of the cylinder can be written as

C S A = 2 π r h

.
Substitute the values,

C S A = 2 π r × 2 r C S A = 4 π r 2

The curved surface area of the cylinder is also

4 π r 2

.
Thus, the ratio of the areas of the sphere and cylinder is 1:1.
Therefore, the correct option is 1.

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