The radius of a sphere is changing at the rate of 01 cm

The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm, is

$8 π c m^{2} s e c$

$12 π c m^{2} s e c$

$160 π c m^{2} s e c$

$200 π c m^{2} s e c$

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Right Answer is: C

SOLUTION

Let r be the radus and S be the surface area of the sphere at any time t. Then,
$S = 4 π r^{2}$
$\Rightarrow \frac{d S}{d t} = 8 π r \frac{d r}{d t} \Rightarrow {(\frac{d S}{d t})}_{r - 200} = 8 π \times 200 \times 0.1 = 160 π c m^{2} / s e c$

The radius of a sphere is changing at the rate of 01 cm

Right Answer is: C

SOLUTION

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