Question : The ratio of the total surface area and volume of a sphere is 2 : 7. Its radius is:
Option 1: 7.5 cm
Option 2: 10.5 cm
Option 3: 10 cm
Option 4: 7 cm
Correct Answer: 10.5 cm
Solution :
Let the radius of the sphere be $r$.
Total surface area of the sphere = $4 \pi r^2$
Volume of the sphere = $\frac{4}{3} \pi r^3$
According to the question,
$4 \pi r^2 : \frac{4}{3} \pi r^3 = 2 : 7$
⇒ $\frac{3}{r} = \frac{2}{7}$
⇒ $r = \frac{21}{2} = 10.5$ cm
Hence, the correct answer is 10.5 cm.
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