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The Radius of a Circular Plate is Increasing at the Rate of 0.01 Cm/Sec. the Rate of Increase of Its Area When the Radius is 12 Cm, is (A) 144 π Cm2/Sec - CBSE (Arts) Class 12 - Mathematics

ConceptRate of Change of Bodies Or Quantities

Question

The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increase of its area when the radius is 12 cm, is

• 144 π cm2/sec

• 2.4 π cm2/sec

•  0.24 π cm2/sec

•  0.024 π cm2/sec

Solution

0.24 π cm2/sec

$\text { Let r be the radius and A be the area of the circular plate at any timet.Then,}$

$A=\pi r^2$

$\Rightarrow\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

$\Rightarrow\frac{dA}{dt}=2\pi\left( 12 \right)\left( 0 . 01 \right)$

$\Rightarrow\frac{dA}{dt} {=0.24\pi \ cm}^2 /sec$

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Solution The Radius of a Circular Plate is Increasing at the Rate of 0.01 Cm/Sec. the Rate of Increase of Its Area When the Radius is 12 Cm, is (A) 144 π Cm2/Sec Concept: Rate of Change of Bodies Or Quantities.
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