Question:
If the radius of a circle is \(r = 6\) cm, then the rate of change of Area with respect to radius is:
If the radius of a circle is \(r = 6\) cm, then the rate of change of Area with respect to radius is:
Show Hint
Differentiate A=πr² to get dA/dr=2πr, then plug in r=6.
Updated On: Sep 23, 2026
- \(10\pi\)
- \(12\pi\)
- \(8\pi\)
- \(11\pi\)
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The Correct Option is B
Solution and Explanation
Step 1: Key Formula or Approach:
The area of a circle is \(A = \pi r^2\). "Rate of change of Area with respect to radius" means \(\dfrac{dA}{dr}\).
Step 2: Differentiating:
\[ \frac{dA}{dr} = 2\pi r \]
Step 3: Substituting \(r = 6\):
\[ \frac{dA}{dr}\Big|_{r=6} = 2\pi (6) = 12\pi \]
Final Answer:
The rate of change of Area with respect to radius at \(r=6\) cm is \(12\pi\). \[ \boxed{12\pi} \]
The area of a circle is \(A = \pi r^2\). "Rate of change of Area with respect to radius" means \(\dfrac{dA}{dr}\).
Step 2: Differentiating:
\[ \frac{dA}{dr} = 2\pi r \]
Step 3: Substituting \(r = 6\):
\[ \frac{dA}{dr}\Big|_{r=6} = 2\pi (6) = 12\pi \]
Final Answer:
The rate of change of Area with respect to radius at \(r=6\) cm is \(12\pi\). \[ \boxed{12\pi} \]
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