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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