The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/ sec  is proportional to

# The rate of change of surface area of a sphere of radius $r$ when the radius is increasing at the rate of  is proportional to

1. A

$\frac{1}{{r}^{2}}$

2. B

$\frac{1}{r}$

3. C

${r}^{2}$

4. D

$r$

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### Solution:

Let be the surface area and be the radius of the

sphere at any time. Then,

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