Question : The total surface area of a solid hemisphere is 1039.5 cm2. The volume (in cm3) of the hemisphere is: (Take $\pi=\frac{22}{7}$)
Option 1: 2425.5
Option 2: 2530.6
Option 3: 2525.6
Option 4: 2225.5
Correct Answer: 2425.5
Solution :
Let $r$ be the radius of the hemisphere.
We know the total Surface Area of the solid hemisphere = $3\pi r^2$
$⇒3\pi r^2 = 1039.5$
$\Rightarrow 3\times \frac{22}{7}\times r^2 = 1039.5$
$\Rightarrow r^2 = 2.25 \times 7\times 7$
$\Rightarrow r = 10.5 \ \text{cm}$
The volume of the hemisphere
= $\frac{2}{3}\pi r^3$
= $\frac{2}{3}\times \frac{22}{7}\times 10.5\times 10.5\times 10.5$
= $ 2425.5 \ \text{cm}^3$
Hence the correct answer is 2425.5 cm
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