Help In A Math Problem Involving Circles And Diameters.

Help with a maths question involving circumference and diameter?

Billy likes to go cycling.
His bike has wheels of diameter 80cm

He has invented a counter for his bike, which counts the number of revolutions the wheels make.

One day the counter shows 170 revolutions

How far has Billy cycled?
Give your answer to the nearest metre

Please help!
Thanks

Diameters of circles?

I'm going to simplify this and take the diameter of the big circle to be R. The radius of the little circle will be r. (Later I'll turn these back into D and d).

If you draw the diagram, the center of the little circle is r away from the wall and floor. That forms a 45-45-90 triangle.

Now look along the diagonal. The center of the small circle is r√2 from the corner. Then you continue another r units and you touch the big circle, then you continue another R units to get to the center of the big circle. This too forms a right triangle (45-45-90) with legs of R. The diagonal will be R√2.

Writing that as an equation:
r√2 + r + R = R√2

Subtract R from both sides:
r√2 + r = R√2 - R
r(√2 + 1) = R(√2 - 1)

Divide both sides by (√2 + 1):
r = R(√2 - 1) / (√2 + 1)

Rationalize the denominator by multiplying by (√2 - 1) on top and bottom:
r = R(√2 - 1)² / (√2 + 1)(√2 - 1)
r = R(√2 - 1)² / [ (√2)² - 1 ]
r = R(√2 - 1)² / (2 - 1)
r = R(√2 - 1)² / 1
r = R(√2 - 1)²

Expand out the squared term:
r = R(2 - 2√2 + 1)

Simplify:
r = R(3 - 2√2)

If you double these you'll get the diameters, but not affect the ratio because d = 2r and D = 2R:
d = D(3 - 2√2)

Answer:
The diameter of the small pipe will be (3 - 2√2) times the diameter of the big pipe:
d = (3 - 2√2)D

P.S. That's about 0.172 or about 17.2% as big as D.

Need help with this problem that involves diameter?

assuming:

A: amount of material in cm^2
a: proportionality constant
d: diameter

so

A = a d^2

452 = a (12^2)

a = 452 / 144

1017 = a (x^2)

x^2 = 1017 / a = 1017 * 144 / 452 = 324

so x = 18 cm

Help with a math problem? (Involves circles)?

First figure out the (x,y) coordinate for the center of the Ferris wheel.

It is 500 feet from the entrance, so x = 500
It is 12 feet off the ground, then another 120 feet (half the diameter), so y = 132

Center (500, 132)
Radius = 240/2 = 120 feet

General formula of a circle with center (xc, yc) and a radius of r:
(x - xc)² + (y - yc)² = r²

Plug in your values:
(x - 500)² + (y - 132)² = 120²

Answer:
(x - 500)² + (y - 132)² = 14400

Math Problems with Circles and other shapes?

Find the Circumference (C) of each Circle to 2 decimal places:

1) diameter = 4.6m 2) Radius = 5.3cm 3) Diameter = 8.2m

Find the diameter (D) Of each Circle to 2 decimal places:

1) Circumference = 28.4m 2) Circumference = 29.7cm 3) Circumference = 11.6m

Find The area of each Circle to 2 decimal places:

1) Radius = 16cm 2) Diameter = 14.8 3) Radius = 47.2

Also I need help with an Octagon and Polygon

The octagon's Radius is 5.3m and One of it's sides are 4.7m. What is the Area of the octagon?

The polygons Radius is 2.4m and One of it's sides are 1.9m. What is the Area of the Polygon?

Math Question involving circles and rectangles?

It really helps to draw a picture.

Basically, because the shorter side of the rectangle is 6 inches (which limits the circle), the diameter of the circle must be 6 inches. The 8 inches does not affect the area of the circle. Half of the diameter is the radius--3 inches. Then you use the formula for the area of a circle.

A = πr²
A = π(3)²
A = 9π inches²

EDIT: I drew a picture of the problem so you can see what I'm talking about: http://www.flickr.com/photos/67911906@N05/7687216916/in/photostream/lightbox/
Notice that the circle only touches three sides (is tangent to three sides), so the 6 inches is the only side that limits the circle's size.

Help on problems about radius, diameter, circumference. etc.?

1) A circle of a diameter has a diameter of 30 ft. Find:
a. The circumference of the circle.
b. The area of the circle.

2) A circle has a diameter of 12.8 m. Find :
a.The circumference of the circle.
b. The area of the circle.

3) The wheels on Sally's bike have a diameter of 27 in. How far does the bike travel with each turn of the wheels?

4) A round table has a diameter of 36 in. How much plastic laminate is needed to cover the top of the table?

5) A criminal has escaped in a train wreck. The police believe he could have traveled no more than 6 miles in any direction from the wreck. How many square miles must be searched?

6) Jeffrey ran 8 laps around a circlular track with a radius of 20 m. How far did she run?