A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is:

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Solution

Q.
A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is:

1 1 : 1

2 1 : 4

3 2 : 3

4 3 : 2

Ans.
(3)

The total surface area of a sphere = $4 π r^{2}$

The surface area of one hemi-sphere = $3 π r^{2}$

$∴$ The total surface area of two hemi-spheres = $6 π r^{2}$

Required Ratio = $\frac{4 π r^{2}}{6 π r^{2}} = \frac{4}{6} = \frac{2}{3}$

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