QQuestion
If the volumes of two spheres are in the ratio 27 : 64, then the ratio of their radii is:
(a) 3 : 4
(b) 4 : 3
(c) 9 : 16
(d) 16 : 9
✓Answer
(a) 3 : 4
Explanation:
The volume of a sphere is proportional to the cube of its radius.
Let the radii be r and R.
\frac{r^3}{R^3}=\frac{27}{64}Taking the cube root:
\frac{r}{R}=\sqrt[3]{\frac{27}{64}}⇒ r/R = 3/4
Therefore, r : R = 3 : 4.
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