Question : The surface area of a sphere is 221.76 cm2. Its volume (in cm3) is (correct to one decimal place):
(Take $\pi=\frac{22}{7}$)
Option 1: 315.6
Option 2: 289.8
Option 3: 280.4
Option 4: 310.5
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Correct Answer: 310.5
Solution :
The total surface area of the sphere = $4\pi r^2$
Where, $r$ = radius of the sphere
According to the question, we have
$4\pi r^2 = 221.76$
$⇒4 \times (\frac{22}{7}) \times r^2 = 221.76$
$⇒ r^2 = 17.64$
$\therefore r = 4.2\ \text{cm}$
Now,
The volume of the sphere =$(\frac{4}{3}) \times \pi \times r^3=(\frac{4}{3}) \times (\frac{22}{7}) \times (4.2)^3= 310.5 \ \text{cm}^3$
Hence, the correct answer is 310.5 cm
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