# Math Help - Expansion of Area of Circle

1. ## Expansion of Area of Circle

A circular cloud of poison gas from a factory explosion is expanding so that t hours after the explosion the radius of the cloud is meters. How fast is the area of the cloud increasing 4 hours after the explosion?
________________________square meters per hour

I've tried about 11 different answers and none of them have worked out, help?

2. The area of the cloud (circle) is $A = \pi r^2$

Substitute R(t) into the formula to get $A(t) = \pi (50+20t)^2$

Differentiate A(t) with respect to t, then substitute t=4 into your equation for $\frac{dA}{dt}$ to get your answer in square metres per hour.