Question : The curved surface area of the sphere is 154 cm2. Find the volume of the sphere (rounded off to one digit after decimal).
Option 1: 156.9 cm3
Option 2: 179.7 cm3
Option 3: 161.1 cm3
Option 4: 147.8 cm3
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Correct Answer: 179.7 cm 3
Solution :
Given, the curved surface area of the sphere is 154 cm
2
Let the radius of the sphere be $r$.
$4πr^2 = 154$
⇒ $4 × \frac{22}{7} × r^2 = 154$
⇒ $r^2 = \frac{49}{4}$
⇒ $r = \frac{7}{2}$
So, the volume of the sphere
$= \frac{4}{3} × \frac{22}{7} × (\frac{7}{2})^3$
$=\frac{4}{3} × 22 × \frac{49}{8}$
$=11 × \frac{49}{3}$
$=\frac{539}{3}$
$=179.7$ cm$^3$
Hence, the correct answer is 179.7 cm$^3$.
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