The rate of change of the area of a circle with respect to its radius r (in cm2/s), when r=6 cm is :
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Step-by-Step Solution
Step 1: Write the formula for the area of a circle
The area of a circle, denoted by A, is given by the formula A=πr2, where r is the radius of the circle. This formula is fundamental for calculating the area based on its radius.
Step 2: Differentiate the area with respect to the radius
To find the rate of change of the area with respect to the radius, we need to differentiate the area formula A=πr2 with respect to r. Using the power rule for differentiation, drd(r2)=2r, so drdA=2πr.
Step 3: Substitute the given radius value
The problem asks for the rate of change when the radius r=6 cm. We substitute this value into the derivative we just calculated. This gives us 2π(6), which simplifies to 12π.