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?
let the radius be r ft
2πr = 157
r = 157/(2π) = 24.987.. ft
area = πr^2 = 1961.5 ft^2
time = 1961.5/400 = appr 4.9 hours
To find the time it would take for Chris to paint the entire stage, we need to first calculate the area of the circular stage.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, we're given the circumference as 157 feet.
We can rearrange the formula to solve for the radius:
2πr = C
r = C / (2π)
Let's substitute the given circumference to find the radius:
r = 157 / (2π) ≈ 25 feet
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Let's calculate the area of the circular stage:
A = π(25^2)
A ≈ 625π square feet
Now, we can determine how long it would take Chris to paint the entire stage by dividing the area of the stage by his painting rate:
Time = Area / Painting rate
Time = (625π) / 400 ≈ 4.90 hours
To the nearest hour, it would take Chris approximately 5 hours to paint the entire stage.