area of a semicircle is increasing at a constant rate. At 5 secs the area is 4pi. At 7 secs the area is 5pi. In terms of r at what rate is the radius changing?

Answer 1

In two seconds, the area increased by π. So,

da/dt = π/2

a = π/2 r²

At t=7, a=5π
5π = π/2 r²
10 = r²
r = √10

a = π/2 r²
da = πr dr/dt
π/2 = π√10 dr/dt
dr/dt = 1/2√10