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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


Team Careers360 12th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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