The circumference of a circular stage is 157 feet. If Chris paints the stage at a rate of 400 square feet per hour, how long would it take to the nearest hour, for Chris to paint the entire stage?

We need the circumference and area of the circle equations:

c = 2*pi*r

a = pi*r^2

lets find the radius from the first equation:

r = c/2*pi

r = 157 / (2*3.14)

r = 24.99 ft

now lets calculate the area:

a = pi*r^2

a = 3.14 * (24.99) ^2

a = 1960.93 ft^2

Now we need to divide the total area by the rate at which Chris paints, and that gives us the time needed:

time = 1960.93/400

time = 4.9 hours

that would be 5 hours rounded to the nearest hour