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If the radius of a sphere is half of the radius of another sphere, then their respective volumes are in the ratio

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1 : 8

2 : 1

1 : 2

4 : 1

answer is A.

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Detailed Solution

Given that the radius of a sphere is half of the radius of another sphere.
Assume that the radius of first sphere be

r

and radius of second sphere be

\frac{r}{2} .

The formula for the volume of sphere is given by,
Volume of sphere

= \frac{4}{3} π r^{3}

\frac{Volume of second sphere}{Volume of first sphere} = \frac{\frac{4}{3} π {(\frac{r}{2})}^{3}}{\frac{4}{3} π r^{3}}

= \frac{1}{8} \times \frac{\frac{4}{3} π r^{3}}{\frac{4}{3} π r^{3}}

= \frac{1}{8} \times 1

= \frac{1}{8}

Therefore, their respective volumes are in the ratio

1 : 8 .

Hence option (1) is correct.

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