Question

A Ferris wheel has a radius of 20 feet. It has 16 carts attached to the center.

Lets try to find the central angle, the arc length, and the area of a sector between the carts.

Answer 1

there are 360 degrees in a circle so each central angle will be 360/16 carts

Answer 2

Each sector is an isosceles triangle which can be thought of as two right triangles back to back. The hypotenuse of these triangles is 20 feet.

Answer 3

Hmm. I see. So we have a central angle of 22.5

Now, I know we can do something with the radius and central angle...

Answer 4

the angle would be 22.44 the arc length would be 2.5pi and the area per sector would be 25pi

Answer 5

for the arc length you calculate the perimeter which is pi*diameter which is 40pi and sivide it between the 16 sections

Answer 6

it is 2.5pi

Answer 7

and for the area you calculate the whole circle: pi*radius^2 which is pi*400 and divide it by the 16 sections you have and its 25pi feet

Answer 8

Well, with the area remember that the ferris wheel is not a circle but a regular polygon.\[\sin{\frac{22.5}{2}} = \frac{h}{2}*\frac{1}{20 feet}\]

Answer 9

well, he said arc length, polygons dont have arcs, do they?

Answer 10

"area of sector between the carts" sounds like a triangle to me.

Answer 11

We're assuming the ferris wheel is a circle.

Answer 12

That's fine. Of course they are made either way. Solve the problem according to whatever the topic of the material you are currently working with.

Answer 13

arc length = 1/16th the circumference of the circle.

Answer 14

Central Angle = 1/16th of 360 degrees
Arc Length = 1/16th the circumference of the circle
Sector Area = 1/16th the area of the circle.

Answer 15

Okay,


So C = 2pir
C = 2(3.14)(20)/16 = 7.85

Answer 16

Salvador, don't use sine or anything to that degree. Slow down and take it from The Central Angle. I understand that and only that so far.

Answer 17

ohhh sorry

Answer 18

then forget what I said, it was a circle after all anyways

Answer 19

in which case it would be
angle=22.5
arc=2.5pi=7.85 ((perimeter=pi*diameter=3.141592*40)/16 sections)
area=25pi=78.5 (area=pi*radius^2=3.141592*400)/16 sections

Answer 20

Where did 25pi come from.

Answer 21

400/16=25

Answer 22

400pi is pi*radius^2, you divide it by the 16 sections so it's 25pi=78.5