If the area of the circular base of a hemisphere is \(308 {cm}^2\), find the volume of the hemisphere
If the area of the circular base of a hemisphere is \(308 {cm}^2\), find the volume of the hemisphere
यदि एक अर्धगोले के वृत्ताकार आधार का क्षेत्रफल $308 \text{ सेमी}^2$ है, तो अर्धगोले का आयतन ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
\(1437.33\sqrt{2} \text{cm}^3\)/ \(1437.33\sqrt{2}\)घन सेंटीमीटर
हम जानते हैं:
वृत्त का क्षेत्रफल = $\pi r^2 = 308$
$\frac{22}{7} \times r^2 = 308$
$r^2 = 98 \Rightarrow r = 7\sqrt{2}$
अब, अर्धगोले का आयतन:
$V = \frac{2}{3} \pi r^3$
$V = \frac{2}{3} \times \frac{22}{7} \times (7\sqrt{2})^3$
$(7\sqrt{2})^3 = 686\sqrt{2}$
$V = \frac{2}{3} \times \frac{22}{7} \times 686\sqrt{2}$
$V = \frac{4312\sqrt{2}}{3}$
$V \approx 1437.33\sqrt{2}$
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