Question

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 R(t)=50+20t meters. How fast is the area of the cloud increasing 5 hours after the explosion?

Answer 1

6000π m²/h

Explanation:

Area of the circular cloud =πr²----------------------------------------- (1)

Radius as a function of time = R(t)=50+20t------------------------ (2)

dA/dt = (dA/dr) x (dr/dt)-----------------------------------------------------(3)

dA/dr = 2πr

dr/dt = 20

After 5 hours, the radius of the cloud will be :

R(5)=50+20(5)

= 150 meters

Substituting into (3)

dA/dt = 2π(150) x 20

= 6000π m²/h