Question : The volume of a solid hemisphere is 19,404 cm3. Its total surface area (in cm2) is:
(Take $\pi=\frac{22}{7}$)
Option 1: 2772
Option 2: 3465
Option 3: 2079
Option 4: 4158
Correct Answer: 4158
Solution :
Let $r$ be the radius of the hemisphere.
Volume of a hemisphere, V = $\frac{2}{3} \pi r^3$
Given: V = $19404$
⇒ $19404 = \frac{2}{3} \pi r^3$
⇒ $19404 = \frac{2}{3}\times \frac{22}{7}\times r^3$
⇒ $r^3= 9261$
⇒ $r = 21\ \text{cm}$
Total Surface Area of the hemisphere = $3 \pi r^2=3 \times \frac{22}{7} \times 21^2= 4158\ \text{cm}^2$
Hence, the correct answer is 4,158 cm
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