The radius of a circle is increasing at the rate of 0.02cms-1. Find the rate at which the area is increasing when the radius of the circle is 7cm.

Answer Details

We know that the formula for the area of a circle is A = πr^2, where A is the area and r is the radius. We are given that the radius of the circle is increasing at the rate of 0.02 cm/s. This means that dr/dt = 0.02 cm/s. We need to find the rate at which the area is increasing when the radius of the circle is 7 cm. This means we need to find dA/dt when r = 7 cm. To do this, we first differentiate the formula for the area of a circle with respect to time: dA/dt = d/dt(πr^2) Using the chain rule, we get: dA/dt = 2πr (dr/dt) Substituting the given values, we get: dA/dt = 2π(7) (0.02) = 0.88π cm^2/s So, the rate at which the area is increasing when the radius of the circle is 7 cm is 0.88π cm^2/s, which is approximately 2.76 cm^2/s. Therefore, the answer is option (D) 0.88cm^2S^-1.