Posted by **David** on Thursday, October 20, 2011 at 1:16pm.

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?

- calculus -
**Steve**, Thursday, October 20, 2011 at 3:30pm
In two seconds, the area increased by π. So,

da/dt = π/2

a = π/2 r^{2}

At t=7, a=5π

5π = π/2 r^{2}

10 = r^{2}

r = √10

a = π/2 r^{2}

da = πr dr/dt

π/2 = π√10 dr/dt

dr/dt = 1/2√10

## Answer This Question

## Related Questions

- AP Biology - After an enzyme is mixed with its substrate, the amount of product ...
- Calculus - The area of a circular oil slick is increasing at a constant rate of ...
- calculus - The radius of the base of a right circular cylinder is r com and the ...
- calculus - Oil spilled from a ruptured tanker spreads in a circle whose area ...
- Calc - Oil spilled from a ruptured tanker spreads in a circle whose area ...
- math - Oil spilled from a ruptured tanker spreads in a circle whose area ...
- math - Oil spilled from a ruptured tanker spreads in a circle whose area ...
- Calculus I - Let A be the area of a circle with radius r that is increasing in ...
- Calculus - How fast is the area of a square increasing when thh side is 3m in ...
- Calculus - A spherical balloon is being inflated and the radius is increasing at...

More Related Questions