Question : The surface area of a sphere is 616 cm2. The volume of the sphere would be:
Option 1: $1437\frac{1}{3}$ cm3
Option 2: $2100$ cm3
Option 3: $2500$ cm3
Option 4: $1225\frac{3}{5}$ cm3
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Correct Answer: $1437\frac{1}{3}$ cm 3
Solution :
Given: The surface area of a sphere = 616 cm$^2$
We know that, The surface area of a sphere of radius $r$ = $4\pi r^2$
⇒ $4\pi r^2$ = 616
⇒ $4×\frac{22}{7}× r^2$ = 616
⇒ $r^2 = \frac{616×7}{4×22}= 49$
⇒ $r = 7$
Now, volume of sphere = $\frac{4}{3}\pi r^3$
= $\frac{4}{3}×\frac{22}{7}×7×7×7$
= $\frac{4312}{3} = 1437\frac{1}{3}$ cm
3
Hence, the correct answer is $1437\frac{1}{3}$ cm$^3$.
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