The owner of a carousel wants to paint the surface of its floor. The paint is very expensive, so he only wants to buy the exact amount needed. He sends his younger son over to measure the the surface area of the carrousel. When the son gets there, he realizes that he cannot measure the exact diameter, because all of the machinery is in the middle of the hole. So, he takes a measurement and leaves. When he arrives at home, he tells his father that he measured 70 feet from one outer edge to the the other side, and the tape measure touched the opening in the center.
His father was furious! How could he be so incompetent?! But his older son soon spoke up: "Father, I know the area of the floor of the carrousel." His father was amazed.
What is the area of the floor of the carrousel? (Show your work :-)
2006-11-21 10:53:10 · 3 answers · asked by Dave 6 in Science & Mathematics ➔ Mathematics
There is enough information to solve this problem. Here's a picture of the solution:
http://mathforum.org/pcmi/hstp/resources/papercup/cup2.revised.gif
The length between points A and B is 70 feet. Good luck!
2006-11-21 15:08:52 · update #1
Take the diagram you were given, and draw in the inner and outer radii such that the inner radius meets the 70 ft line in a right angle and the outer radius hits one end of the 70 ft line. Mark the right angle, and then you'll see that the outer radius is the hypotenuse of a right triangle formed by the inner radius and half of the 70 ft line. Thus, you have r_inner^2 + 35^2 = r_outer^2 ==> r_outer^2 - r_inner^2 = 35^2 = 1225. Now, the area of an annular region such as this would be equal to the area of the inner circle subtracted from the area of the outer circle, or pi*r_outer^2 - pi*r_inner^2 = pi*(r_outer^2 - r_inner^2) = 1225*pi = 3,848 ft^2. It turns out that the inner and outer radii don't need to be measured. Any annular region with a chord of length 2L that is tangent to the inner circle will have an area equal to that of a circle with radius L.
2006-11-28 08:36:31 · answer #1 · answered by DavidK93 7 · 2⤊ 0⤋
I don't think you've given enough infomation. how big is the diameter of the hole in the middle? the 70 feet could be anywhere from the diameter of the carousel. maybe i don't get it!
2006-11-21 19:02:10 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Area = Pi x R squared
3.14 (Pi) x 1225 (35x35) = 3846.50 sq feet
R (radius) = 35, which is half the diameter ( D = 70ft )
2006-11-21 19:18:27 · answer #3 · answered by DixieNormus 4 · 1⤊ 1⤋