Question : The total surface area of a solid hemisphere is $942 \mathrm{~cm}^2$. Its volume (in $\mathrm{cm}^3$ ) is closest to:
(Take $\pi=3.14$ )
Option 1: 2089
Option 2: 2093
Option 3: 2037
Option 4: 2097
Correct Answer: 2093
Solution :
Given: The total surface area of a solid hemisphere = $942\ cm^2$
$3 \pi r^2=942$
⇒ $3\times 3.14\times r^2=942$
⇒ $3.14\times r^2=314$
⇒ $ r^2=100$
⇒ $ r=10$
Volume of hemisphere = $\frac{2}{3}\pi r^3$
= $\frac{2}{3}\times 3.14\times10\times10\times10$
= $\frac{6280}{3}$
= $2093.33 \approx 2093$ cm
3
Hence, the correct answer is 2093 cm
3
.
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