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Answer (Detailed Solution Below)

Option 1 : $1386\ \text{cm}^2$ / $1386\ \text{cm}^2$

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Detailed Solution

सही उत्तर $1386\ \text{cm}^2$ / $1386\ \text{cm}^2$ है।

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PrepSnapprepsnap.in • Part -A

Question:

The volume of a solid sphere is $4851\ \text{cm}^3$. Its total surface area is / एक ठोस गोले का आयतन $4851\ \text{cm}^3$ है। इसका कुल पृष्ठीय क्षेत्रफल है

1.
$1386\ \text{cm}^2$ / $1386\ \text{cm}^2$
2.
$1232\ \text{cm}^2$ / $1232\ \text{cm}^2$
3.
$1540\ \text{cm}^2$ / $1540\ \text{cm}^2$
4.
$1078\ \text{cm}^2$ / $1078\ \text{cm}^2$

Correct Answer: $1386\ \text{cm}^2$ / $1386\ \text{cm}^2$

$V = \frac{4}{3}\pi r^3 = 4851$ gives $r^3 = \frac{4851 \times 3}{4\pi} = 1157.6$, so $r = 10.5\ \text{cm}$. Surface area $= 4\pi r^2 = 4 \times \frac{22}{7} \times 10.5^2 = 1386\ \text{cm}^2$. / $V = \frac{4}{3}\pi r^3 = 4851$ से $r^3 = \frac{4851 \times 3}{4\pi} = 1157.6$, अतः $r = 10.5\ \text{cm}$। पृष्ठीय क्षेत्रफल $= 4\pi r^2 = 4 \times \frac{22}{7} \times 10.5^2 = 1386\ \text{cm}^2$।

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