The circumference of a circular stage is 157 feet. if katie paints the stage at the rate of 400 square feet per hour hownlong would it take, to the nearest hour

To answer this question you will need to use the information about the circumference to find the area.

Solve for the diameter using the circumference formula.
C = pi x d
157 = 3.14 x d
d = 50 feet

Now use the diameter to find the radius (50/2) of 25 feet.

You can now find the area of the stage.

A = pi x r^2
3.14 x 25^2
A = 1962.5 square feet

To find out how many hours it will take to paint divide the tots area by the number of square feet she can paint per hour.

1962.5/400 = 4.9

Katie will take approximately 5 hours to paint the stage.