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  • need solution for RD Sharma maths class 12 chapter Derivative As a Rate Measure exercise 12.2 question 31

need solution for RD Sharma maths class 12 chapter Derivative As a Rate Measure exercise 12.2 question 31

Answers (1)

Answer: \frac{d A}{d t}=0.32 \pi \: cm^{2}/sec 

Hint: We know the area of the circle A=\pi r^{2}

Given: Disc of radius 3 cm is being heated.

It radius increases at the rate of 0.05 cm/sec

Solution: Differentiating both side with respect to t .

\frac{d A}{d t}=\frac{d\left(\pi r^{2}\right)}{d t}=\pi \times 2 r \frac{d r}{d t}.....…(i)

As per the given criteria the circular disc expands on heating with the rate of change of radius is 0.05 cm/sec.

\frac{d r}{d t}=0.05\: cm/sec

Substitute the value in equation (i)

We get,

\begin{aligned} &\frac{d A}{d t}=\pi \times 2 r \times 0.05 \\\\ &\frac{d A}{d t}=\pi \times 3.2 \times 2 \times 0.05 \\\\ &\frac{d A}{d t}=0.32 \pi\; cm^{2}/sec \end{aligned}

 

 

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