Your town is building a circular ice rink with a diameter of 100 feet. Around the ice rink will be a walkway that is 10 feet wide. What is the approximate area of the walkway?
To find the approximate area of the walkway around the circular ice rink, we need to subtract the area of the ice rink from the area of the entire circle including the walkway. Here are the steps to solve the problem:
1. Find the radius of the circular ice rink. The radius is half the diameter. In this case, the radius is 100 feet divided by 2, which is 50 feet.
2. Calculate the area of the entire circle including the walkway. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the radius is 50 feet, so the area of the entire circle is approximately 3.14 * (50)^2 square feet.
3. Find the area of the ice rink. Again, use the formula A = πr^2, where A is the area and r is the radius. The radius of the ice rink is 50 feet, so the area of the ice rink is approximately 3.14 * (50)^2 square feet.
4. Subtract the area of the ice rink from the area of the entire circle to get the approximate area of the walkway.
By following these steps and performing the calculations, you can find the approximate area of the walkway around the circular ice rink.
the area of the walkway is the whole area minus just the rink, so that's
πR^2-πr^2 = π(R^2-r^2) = π((50+10)^2-50^2) = π(60^2-50^2) = π(3600-2500) = 1100π ft^2