Precalc question

Question

A water treatment facility operates by dripping water from a 60 foot long arm whose end is mounted to a central pivot. The water then filters through a layer of charcoal. The arm rotates once every 8 minutes.

(a) Find the area of charcoal covered with water after 1 minute.

(b) Find the area of charcoal covered with water after 1 second.

(c) How long would it take to cover 100 square feet of charcoal with water?

(d) How long would it take to cover 3245 square feet of charcoal with water?

Answer 1

Hi Flora H.,

If this question is stumping you, you might need some tutoring on basics? I'll give you some concise pointers here which may help you, but if that's not enough, get some 1-on-1 help, please. You need to "get" the concept of proportions thoroughly!

"Central pivot" and "arm" should set up the idea of a circular path for you. Since the question is referring to "area" of charcoal, a reasonable assumption might be that the entire arm drips water, i.e. not just from the tip (which would cover an indeterminate area of charcoal). OK, then, the arm sprinkles a complete circle in 8 minutes; can you figure the area of that circle? (Use your circle area formula!)

Then just extend that proportion (circle area : time) for other periods of time to obtain other areas-covered, or for other area-covered to obtain other times. For example, 1 minute is (1/8) of 8 minutes, so the area covered will be (1/8) that of the entire circle area.

--Cheers, -- Mr. d.

Answer 2

Hi Flora H.,

If this question is stumping you, you might need some tutoring on basics? I'll give you some concise pointers here which may help you, but if that's not enough, get some 1-on-1 help, please. You need to "get" the concept of proportions thoroughly!

"Central pivot" and "arm" should set up the idea of a circular path for you. Since the question is referring to "area" of charcoal, a reasonable assumption might be that the entire arm drips water, i.e. not just from the tip (which would cover an indeterminate area of charcoal). OK, then, the arm sprinkles a complete circle in 8 minutes; can you figure the area of that circle? (Use your circle area formula!)

Then just extend that proportion (circle area : time) for other periods of time to obtain other areas-covered, or for other area-covered to obtain other times. For example, 1 minute is (1/8) of 8 minutes, so the area covered will be (1/8) that of the entire circle area.

--Cheers, -- Mr. d.