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Can you find the area of the carrousel floor?
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 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 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: "I know the area of the floor of the carrousel." His father was amazed.
What is the area of the floor of the carrousel? There is enough information to solve this problem. Here's a picture of the solution:
http://mathforum.org/pcmi/hstp/resources/papercup/...
The length between points A and B is 70 feet. Good luck!
6 Answers
- Scott RLv 61 decade agoFavorite Answer
1225π ft^2
Picture:
http://mudandmuck.com/str2/cup2.revised.gif
r = radius of small circle
R = radius of Carousel
35^2 + r^2 = R^2
1225 = R^2 - r^2
area of floor to paint = (Area of carousel - area of small circle (machinery in the way)) = πR^2 - πr^2 = π(R^2 - r^2) = 1225π
- hayharbrLv 71 decade ago
If R = the radius of the carousel and r = the radius of the hole, draw a perpendicular segment to the middle of the 70 ft chord that ends at the center. Its length is r . The area needing to be painted is piR^2 = pir^2, or pi(R^2 - r^2).
But by Pythagorean Theorem, R^2 - r^2 is 35^2
So the area needing to be painted is pi (35^2) sq feet.
- stephen mLv 41 decade ago
Call the big radius R and the small radius r. You want to work out ÏR^2 - Ïr^2 = Ï(R^2 - r^2).
Draw in the small radius from the centre, perpendicular to the given line, as well as a big radius from the centre to the end of the given line. That gives you a right angled triangle with hypotenuse R, and sides r and 35. So R^2 - r^2 = 35^2, so the answer is Ï*35^2.
- 1 decade ago
R = total radius; r = inner radius (radius of center part)
c^2 = R^2 + R^2
R=49.5 ft
r = 1/2 * sqrt(4*R^2 - c^2)
r = 35 ft
R(outer)^2 = R^2 - r^2
A = Ï * 1225.25 ft^2
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- 1 decade ago
i think the answer is either 1225pie or 3846.5 depending on whether or not your teacher wants you to multiply it by pie.
