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Word Problems

Browse Middle School Conic Sections/Circles
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Circle formulas - area, circumference.
    Is a circle a polygon?
    Why is a circle 360 degrees?

Hands of a Clock [10/10/1997]
How many times do the hour and minute hands cross in a 12-hour period of time?

13 Point Circle [8/26/1996]
Is there an easy way to find out how many lines it takes to connect every point on a 13 point circle with every other point on the circle?

Accuracy in Measurement [02/08/2002]
Since pi is irrational, either the circumference or the diameter of a circle must be irrational. How is that possible?

Approximating Pi using Geometry [08/12/1998]
I need to know a simple method to find the approximate value of pi using elementary geometry.

Archimedes' Method of Estimating Pi [5/29/1996]
What was Archimedes' method for estimating pi using inscribed and circumscribed polygons about a circle?

Are Angles Dimensionless? [08/31/2003]
If you look at the dimensions in the equation arc length = r*theta, it appears that angles must be dimensionless. But this can't be right. Or can it?

Area of a Circle Segment [04/18/1999]
What are the steps for figuring out the area of a segment of a circle?

Area of a Circle with Radius less than 1 [02/18/2002]
If the radius is less than 1 it just gets smaller and you get a smaller area...

Area of Inscribed Circle [12/01/1998]
Find the area of the circle inscribed in a triangle ABC using Heron's Law.

Barycenter [08/30/1997]
I need to know the definition of barycenter and how to find it.

Calculating the Radius from a Chord [08/18/1998]
If I know the chord length and chord height, is there a formula for determining the radius of the circle?

Can a Circle be a Polygon? [5/22/1996]
Could a circle be considered a polygon with an infinite number of sides?

Chords of Circles [02/28/2001]
Given a circle with radius 10 and chord XY 8cm long, how far is the chord from the center of the circle?

Circle Area and Square Units [11/12/1997]
Is pi metres squared the same as 10,000 pi centimetres squared? Does a square with sides of 10m have an area of 10m squared or 100 square metres - or are these the same?

Circle Definitions [04/29/2002]
Define a circle and its parts: diameter, radius, center, circumference.

Circles and Squares [4/3/1996]
Given a large circle with a square inside it (the sides of the square are equal to the radius of the larger circle and are chords of the circle) and a smaller circle inside the square...

Circumference and Diameter [8/10/1996]
If you know the circumference of a circle, how do you find the diameter?

Circumference of a Circle Given Chord Length [9/11/1996]
Given the length of a chord of a circle, is it possible to determine the circumference?

Circumference of a Circle, Value of 5! [5/15/1996]
The area of a circle is 16 pi. What is the circumference of the circle? Also, what is the value of 5!?

Clockwise and Counterclockwise [03/19/2001]
What does clockwise mean?

Connection Between Circumference and Surface Area [05/08/1998]
Can you explain the connection between the circumference of a circle and the surface area of a sphere?

Constructing an Ellipse [04/15/1997]
How do you draw an ellipse?

Convert Degrees to Radians [7/21/1996]
How do you convert degrees to radians, and vice versa?

Converting RPM to MPH and MPH to RPM [04/07/2002]
What is the formula for converting RPM's from an 'X' inch diameter wheel into miles per hour?

Convex Polygons and Other Questions [1/22/1996]
A 7th grade geometry class asks some questions about area and perimeter.

Cutting a Circle out of a Square [2/14/1996]
What is the area (to the nearest square centimeter) of the largest circle that can be cut from a square piece of sheet metal 73cm. on each side? Explain how you determined this.

Degrees in a Circle [09/22/1997]
Why does a circle measure 360 degrees - is there a special reason for this calculation?

Deriving the Area Formula for a Circle [03/08/2000]
Why is the area of a circle the square of the radius times pi?

Determining the Equation of a Circle [05/12/2000]
How can I determine which of five equations describes the set of all points (x,y) in the coordinate plane that are a distance of 5 from the point (-3,4)?

Diameter of the Base of a Cone [08/12/1998]
How do you find the formula to calculate the diameter of the base of a cone of nine degrees at various lengths?

Difference between Oval and Ellipse [10/18/2001]
What is the difference between an oval and an ellipse? Am I right if I say that "all ellipses are ovals, but all ovals cannot be ellipses"?

Difference in Radius, Difference in Speed [06/25/2002]
What is the difference in speed between a point on the tread of a tire and another point closer to the center, if the tire is rotating at 5000 rpm?

Distance Between Points of Tangency [03/20/1999]
What is the distance between the contact points of two smaller circles in contact with a larger circle...?

Dividing a Circle into Eleven Pieces [03/03/2002]
Can you divide a circle into 11 pieces using only four straight lines?

Do Circles Have Corners? [08/06/1999]
Can you have angles or corners without edges?

Drawing a Circle without a Compass or Protractor [3/23/1996]
My teacher has asked us to find out how to draw a circle without using either a compass or a protractor. How do I do this?

Ellipse Area and Circumference [04/19/2001]
How can I draw an ellipse and find the area and circumference?

Enclosed Curve [9/9/1996]
What is the name for an enclosed figure in which all the sides are irregularly shaped curves?

Escaping the Tiger [07/10/2003]
A man stands in the center of a circle. On the circumference is a tiger that can only move around the circle. The tiger can run four times as fast as the man. How can the man escape the circle without being eaten by the tiger?

Everyday Uses of Conics [05/24/1999]
Are there any interesting everyday uses for parabolas, ellipses, or hyperbolas?

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