Question : The radius of two spheres is in the ratio of 1 : 5. What is the ratio of the volume of the two spheres?
Option 1: 8 : 27
Option 2: 1 : 25
Option 3: 1 : 125
Option 4: 1 : 64
Correct Answer: 1 : 125
Solution :
Let the radii r
1
= $k$ and r
2
= 5$k$
According to the question,
⇒ Volume of sphere 1 (V1) = $\frac{4}{3}\pi k^{3}$
⇒ Volume of sphere 2 (V2) = $\frac{4}{3}\pi (5k)^{3}$ = $\frac{4}{3}\pi (125)k^{3}$
⇒ Ratio of volumes = $\frac{V1}{V2}$ = $\frac{\frac{4}{3}\pi k^{3}}{\frac{4}{3}\pi (125)k^{3}}$ = $\frac{k^{3}}{125 k^{3}}$ = $\frac{1}{125}$
Hence, the correct answer is 1 : 125.
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