Mathematics 2002 JAMB Past Questions - Question 11: A circle with a radius 5cm has its radius increasing at the rate of 0.2cms¯Ë¡. What will be the corresponding increase in the area?

Correct Answer

A

Explanation

To find the corresponding increase in the area of a circle when the radius is increasing at a given rate, we can use the formula for the derivative of the area of a circle with respect to its radius.The formula for the area of a circle is A = πr², where A is the area and r is the radius.Taking the derivative of both sides with respect to r:dA/dr = 2πrNow, we can substitute the given values into the equation. The radius is increasing at a rate of 0.2 cm/s, so dr/dt = 0.2 cm/s. The radius of the circle is 5 cm, so r = 5 cm.Substituting these values into the equation:dA/dt = 2π(5)(0.2)dA/dt = 2π(1)dA/dt = 2πTherefore, the corresponding increase in the area of the circle is 2π square centimeters.