Question : The total surface area of a solid hemisphere is 4158 cm2. Find its volume (in cm3).
Option 1: 462
Option 2: 9702
Option 3: 1848
Option 4: 19404
Correct Answer: 19404
Solution : Given: total surface area of solid hemisphere = 4158 cm 2 Let the radius of the hemisphere be $r$. The total surface area of a solid hemisphere = $3\pi r^2$ ⇒ $3\pi r^2=4158$ ⇒ $3×\frac{22}{7}×( r)^2=4158$ ⇒ $(r)^2=441$ $\therefore r=21$ Now, volume of hemisphere =$\frac{2}{3}× \pi r^3$ = $\frac{2}{3}×\frac{22}{7}×r^3$ = $\frac{2}{3}×\frac{22}{7}×21×21×21$ = $19404$ cm 3 Hence the correct answer is 19404 cm 3 .
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