Using R, provide the solution for any exercise in either Chapter 4 or Chapter 7 of the calculus textbook. If you are unsure of your solution, post your concerns.

Question 3, page 179
3. Water flows onto a flat surface at a rate of 5cm3/s forming a circular puddle 10mm deep. How fast is the radius growing when the radius is: (a) 1 cm? (b) 10 cm? (c) 100 cm?

radius_change_rate <- function(r) {
  dV_dt <- 5  
  pi <- 3.141592653589793
  dr_dt <- dV_dt / (2 * pi * r)
  return(dr_dt)
}

rate_1cm <- radius_change_rate(1)
rate_10cm <- radius_change_rate(10)
rate_100cm <- radius_change_rate(100)

rate_1cm 
## [1] 0.7957747
rate_10cm 
## [1] 0.07957747
rate_100cm 
## [1] 0.007957747