The area A of a circle is related to its radius by the equationA- r2- The change in area with respect to the radius is x- m- When the radius is 5 m- find the value of x-

The (instantaneous) rate of change of the area with respect to the radius is dAdr=2πr When r=5 m, the area is changing at the rate of nbsp; =(π )10 = 10π m ...

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Standard XII

Physics

Differentiation

The area A of...

Question

The area $A$ of a circle is related to its radius by the equation
$A = π r^{2}$ . The change in area with respect to the radius is $x \times π$ $m$ . When the radius is $5 m$ , find the value of $x$ .

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Solution

The (instantaneous) rate of change of the area with respect to the radius is
$\frac{d A}{d r} = 2 π r$

When $r = 5 m,$
the area is changing at the rate of = $(π) 10 = 10 π m^{2} / m$

$∴ x = 10$

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The area A of a circle is related to its radius by the equation A=πr2. The change in area with respect to the radius is x×π m. When the radius is 5 m, find the value of x.

The (instantaneous) rate of change of the area with respect to the radius is dAdr=2πr When r=5 m, the area is changing at the rate of =(π)10=10π m2/m ∴x=10

The area $A$ of a circle is related to its radius by the equation
$A = π r^{2}$ . The change in area with respect to the radius is $x \times π$ $m$ . When the radius is $5 m$ , find the value of $x$ .

The (instantaneous) rate of change of the area with respect to the radius is
$\frac{d A}{d r} = 2 π r$

When $r = 5 m,$
the area is changing at the rate of = $(π) 10 = 10 π m^{2} / m$

$∴ x = 10$