Question

the area of circle is given by A=πr2 , where r is the radius of the circle. calculate the rate of increase of area with respect to radius​

Answer 1

Answer:

Step-by-step explanation:

Area of the circle =πr2cm2

Radius of the circle =4cm.

A=πr2

Differentiating w.r.t r we get,

dAdr=2πr

Substituting for r we get,

=2×π×4

=8πcm2/cm

Answer 2

As per the data given in the above question.

We have to find the rate of increase of area with respect to radius.

Given,

$Area \: of \: circle,A = πr²$

Step-by-step explanation:

The area of circle is πr².

where

r = radius of the circle.

Now ,the rate of increase means we have differentiate the function.

$A = πr²$

Differentiate the term with respect to r,

$\frac{d}{dr} A = \frac{d}{dr} πr²$

The term π is constant , so take it as a common

$\frac{dA}{dr} = \pi \: \frac{d}{dr} r² \: \: \: \: \: \: ...(1)$

We use the Formula ,

${x}^{n} = n \: {x}^{n - 1}$

Use the Formula in equation (1),

$\frac{dA}{dr} = \pi \:2 \: {r}^{2 - 1} \frac{dr}{dr}$

$\frac{dr}{dr} = 1$

$\frac{dA}{dr} = \pi \times \: 2 \times r$

Hence,

$\frac{dA}{dr} =2\pi \: r$

Project code #SPJ3