SOLUTION: Suppose that during a storm rain is falling at a rate of 1 inch per hour. The water coming from a circular roof with a radius of 20 feet is running down a downspout that can acco

Algebra ->  Functions -> SOLUTION: Suppose that during a storm rain is falling at a rate of 1 inch per hour. The water coming from a circular roof with a radius of 20 feet is running down a downspout that can acco      Log On


   

Question 322506: Suppose that during a storm rain is falling at
a rate of 1 inch per hour. The water coming from a circular
roof with a radius of 20 feet is running down a downspout that can accommodate 400 gallons of water
per hour.
(a) Determine the number of cubic inches of water
falling on the roof in 1 hour.
(b) One gallon equals about 231 cubic inches. Write a
formula for a function g that computes the gallons of
water landing on the roof in x hours.
(c) How many gallons of water land on the roof during
a 2.5-hour rain storm?
(d) Will one downspout be sufficient to handle this
type of rainfall? How many downspouts should there
be?
your help is well needed!
Cheers
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
The roof radius is given in feet. Convert that to inches
20*12=240 inch radius. The area of the roof in square inches is then
pi*(240)^2=57600pi=180955.74 in^2/hour.
Since the rain falls at an inch an hour, we also have 57600Pi cubic inches of rain in one hour.
A gallon is 231 of these. So, in one hour 57600Pi%2F231=783.36 gallons per hour.
Now, you should be able to finish the last few parts of the problem.