1(vii)
The total surface area of a solid sphere (S1) and a solid hemisphere (S2), as shown in the diagram, are equal. The ratio of radii R and r is :
- (a)1 : 1
- (b)2 : 1
- (c)$\sqrt3$ : 2
- (d)2 : $\sqrt3$
Show SolutionHide Solution↓
Let the radius of the sphere (S1) be R and hemisphere (S2) be r.
Total surface area of sphere = 4πR2
Total surface area of hemisphere = 3πr2
Given,
Since, total surface area of sphere and hemisphere are equal,
4πR2 = 3πr2
$\frac{R^2}{r^2} = \frac{3}{4}$
$\frac{R}{r} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2} = \sqrt{3} : 2$.
Hence, option 3 is the correct option.