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If the radii of two spheres are in the ratio 1 : 4, then their surface areas are in the ratio :
Answer & Solution
Correct Answer:
Option
D
Let the radii of the two spheres be r and 4r respectively.
Then,
Required ratio :
$$\eqalign{ & = \frac{{4\pi {r^2}}}{{4\pi {{\left( {4r} \right)}^2}}} \cr & = \frac{{{r^2}}}{{16{r^2}}} \cr & = \frac{1}{{16}} \cr & = 1:16 \cr} $$
Then,
Required ratio :
$$\eqalign{ & = \frac{{4\pi {r^2}}}{{4\pi {{\left( {4r} \right)}^2}}} \cr & = \frac{{{r^2}}}{{16{r^2}}} \cr & = \frac{1}{{16}} \cr & = 1:16 \cr} $$
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