If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius.
If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius.
यदि एक अर्धगोले का कुल पृष्ठीय क्षेत्रफल $462 \text{ सेमी}^2$ है, तो उसकी त्रिज्या ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
7 cm
Total surface area of a hemisphere
$= 3\pi r^2$
Given,
$3\pi r^2 = 462$
Using $\pi = \frac{22}{7}$,
$3 \times \frac{22}{7} \times r^2 = 462$
$\frac{66}{7} r^2 = 462$
Multiply both sides by 7:
$66r^2 = 462 \times 7$
$66r^2 = 3234$
$r^2 = 49$
r = 7 cm
Answer: The radius is 7 cm.
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