The rate of change of the area of a circle with respect to its radius r, when r = 3cm, is: Option 1: 6 cm^2/cm Option 2: 4 cm^2/cm Option 3: 2 cm^2/cm Option 4: 3 cm^2/cm

Answer: 6 cm^2/cm. Solution: The area of a circle is: A = r^2 The rate of change of area with respect to radius is dA/dr. dA/dr = d/dr( r^2) dA/dr = 2 r When r = 3 cm: dA/dr|_(r=3) = 2 (3) = 6 cm²/cm Therefore, the rate of change of the area of a circle with respect to its radius when r = 3 cm is 6 cm²/cm.

Calculus

Application of Derivatives

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applied

The rate of change of the area of a circle with respect to its radius $r$ , when $r = 3$ cm, is:

$6\pi$ $cm^2/cm$

$4\pi cm^2/cm$

$2\pi$ $cm^2/cm$

$3\pi$ $cm^2/cm$

✅ Correct Option: 1

The area of a circle is:

$A = \pi r^2$

The rate of change of area with respect to radius is $\frac{dA}{dr}$ .

$\frac{dA}{dr} = \frac{d}{dr}(\pi r^2)$

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

When $r = 3$ cm:

$\frac{dA}{dr}\bigg|_{r=3} = 2\pi (3)$

$= 6\pi$ cm²/cm

Therefore, the rate of change of the area of a circle with respect to its radius when $r = 3$ cm is $6\pi$ cm²/cm.

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CUET Mathematics Past Year Questions (Topic-Wise)

The rate of change of the area of a circle with respect to its radius $r$ , when $r = 3$ cm, is: