Question 17 of 82beginner🔧 ApplyMCQ1 mark

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is

Exercise: EXERCISE 6.1 | Q: 17 | (Page 5)
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Explanation

The problem asks for the rate of change of the area of a circle with respect to its radius. According to Example 1 in the provided text, the area A of a circle is given by A = πr². The rate of change of area with respect to radius is the derivative dA/dr. Differentiating A = πr² with respect to r gives dA/dr = 2πr. Substituting r = 6 cm into this expression yields 2π(6) = 12π, which corresponds to Option B.

Solution Steps

  1. Step 1: Write the formula for the area of a circle: A = πr².

  2. Step 2: Differentiate the area with respect to the radius r to find the rate of change: dA/dr = d/dr(πr²) = 2πr.

  3. Step 3: Substitute the given value r = 6 cm into the derivative: dA/dr = 2π(6) = 12π.

  4. Step 4: Compare with the given options. The calculated value 12π matches Option (B).

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