Question

A carnival ride is in the shape of a wheel with a radius of 30 feet. The wheel has 30 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit. (8 points)
Answer

Answer 1

Plz help me

Answer 2

I so got you! First in order to find the central angle measure, you divide the circle into 30 equal angles. Because all the angles in a circle measure up to equal 360, to find the measure of one of the angles, divide 360 by 30. This gives you 12. Each of the 30 angles equals 12 degrees. The measure of the arc that is intercepted by a CENTRAL angle (which these all are because they radiate from the center of the circle) is found with the formulaSorry for the lame writing! That means, in words, that the LENGTH of the arc AB is equal to the MEASURE of the arc AB divided by 360, all multiplied by 2 pi r, which is the circumference of the circle, if you remember that formula! So let's fill in what we know. First remember that the measure (which is in degrees) is equal to the measure of the central angle it is enclosed by. The measure of one angle is 12 degrees, so the measure of the arc is also 12. Divide that by 360 and get .033333....Now multiply that by 2 pi r. R is the radius of 30 feet. Since it says that you need the answer in decimal form, use 3.14 for pi. Here's your set up:\[.0333\times2\times3.14\times30=6.27\]That's the arc LENGTH and it is in feet. Length will always be in a measure like feet, or inches or meters. MEASURE will either be in degrees or radians. Try to remember the difference. Now for the area of the sector. That is equal to the measure of the arc length divided by 360, all multiplied by pi times r^2. So we know the arc measure is 12, right? Same as before. 12/360 = .03333.\[A=.0333\times3.14\times(30)^{2}=94.11\]I hope some of that helps you!!