Question

(i) If the area of the circle increases at a constant rate of 4 miles squared per hour, how fast is the radius of the spill increasing when the area is 15 miles squared

Answer 1

Explanation:

Given

Area of a circle = πr²

Calculate radius r

15 = πr²

r² = 15/π

r² = 15/3.14

r² = 4.78

r = √4.78

r = 2.19miles

From the formula:

dA/dt = dA/dr • dr/dt

dA/dt = 2πrdr/dt

Given

dA/dt = 4mi²/hr

r = 2.19miles

Substitute

4 = 2(3.14)(2.19)dr/dt

4 = 13.75dr/dt

dr/dt = 4/13.75

dr/dt = 0.291mi/hr

Hence the rate at which the spill is increasing is 0.291mi/hr