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  • The radius of a circle is increasing at the uniform rate of 3 cm/sec. At the instant when the radius of the circle is 2 cm, its area increases at the rate of _____________<img alt="cm^2/s." src="https://learn.careers360.com/latex-image/?cm%5E

The radius of a circle is increasing at the uniform rate of 3 cm/sec. At the instant when the radius of the circle is 2 cm, its area increases at the rate of _____________cm^2/s.

 

 
 
 
 
 

Answers (1)

\\ $ Area A $ = \pi r^2 \\

\\ \frac{dA}{dt} = 2\pi r\frac{dr}{dt} \\ $ Given: $ \frac{dr}{dt} = 3 $ cm/sec

\\ \frac{dA}{dt} = 2\pi \times 2 \times 3 = 12 \pi \ \ cm^2/sec\\

Hence area increases at the rate 12 \pi cm^2/s.

Posted by

Safeer PP

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