Ask Dr. Math

High School Archive

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

Selected answers to common questions:
    About ellipses.
    Find the center of a circle.
    Is a circle a polygon?
    Volume of a tank.
    Why is a circle 360 degrees?

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1/4 Tank Dipstick Problem (from Car Talk) [12/04/2002]

The gauge on Rick's 18-wheeler is broken, so he uses a dowel to measure the diesel in his tank, which is cylinder-shaped, 20 inches in diameter, and sits on its side. How can he mark the dipstick to show 1/4 of a tank of fuel?

Hands of a Clock [10/10/1997]

How many times do the hour and minute hands cross in a 12-hour period of time?

One Circle Revolving Around Another [05/26/1999]

How many revolutions will a smaller circle make while rotating around the perimeter of a larger 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?

Accurate Drawing of an Ellipse [02/14/1999]

Draw an ellipse accurately using simple tools.

Algebraic Spirals [5/19/1995]

I have read about "algebraic" spirals called "cissoid" and "conchoid," which Descartes deemed more exact than the "transcendental" logarithmic and Archimedean spirals, but I have not been able to find any other information on these figures.

Analytic Geometry [08/31/1997]

How do I find the standard equations of the circles that pass through (2,3) and are tangent to both the lines 3x - 4y = -1 and 4x + 3y = 7?

Analytic Proof that Midpoints Form a Circle [03/10/1998]

Analytic proof that midpoints between a point within a circle and its circumference form a circle.

Angle Inscribed in a Semicircle [11/07/2001]

Prove that any angle inscribed in a semicircle is a right angle.

Angle Measurements of Triangles inside Semicircle [11/26/1998]

If the area of a triangle inside a semicircle is equal to the area outside the triangle within the semicircle, then find the values of the acute angles in the triangle.

Another Grazing Cow [6/7/1995]

A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing?

Applications of Parabolas [10/24/2000]

How are parabolas used in real life?

Approximating Pi using Geometry [08/12/1998]

I need to know a simple method to find the approximate value of pi using elementary geometry.

Arbelos Construction [03/10/2000]

Is there a Euclidean construction for the circles that are sandwiched in the Arbelos?

Arc Formulas [05/08/2003]

I am trying to determine the angle of an arc from the radius and arc length. The radius is 630 and the arc length is 66.82.

Archimedes and the Area of a Circle [09/17/1997]

How do you find the area of a circle without pi?

Archimedes' Method of Estimating Pi [5/29/1996]

What was Archimedes' method for estimating pi using inscribed and circumscribed polygons about a circle?

Arcs Inside a Square [07/25/1999]

What is the area of the figure created by the intersection of two arcs drawn in a square of sidelength 5 units?

Area and Perimeter in Polygons [06/24/1999]

How can I prove the formula A = (a^2n)/(4tan(180/n)) for computing the area of a regular n-gon with sidelength a? How does this compare to the area of a circle?

Area, Angle of Chords of a Circle [7/25/1996]

Calculate the angles PAB and POB, the area of the sector bounded by OP, OB and the minor arc PB.

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 a Crescent [11/10/2000]

What is the formula for the area of a crescent?

Area of a Curved Figure [07/26/1997]

How can you find the area of a curved figure without using calculus?

Area of an Annulus [10/13/2001]

How can I find the area of an annulus?

Area of an Ellipse [08/18/1999]

How do you calculate the area of an ellipse?

Area of an Ellipse Cut by a Chord [05/26/2000]

How can you calculate area of the part of an ellipse cut off by a chord, if you know the major and minor axes, and the chord?

Area of an Ellipse using Integral Calculus [11/4/1996]

How do you find the area of an ellipse?

Area of an Ellipse without using Calculus [11/28/1997]

How do you find the area of an oval without using calculus?

Area of an Oval [11/30/2001]

How do I figure out the area of an oval 17" x 38"?

Area of a Parabola [09/05/1997]

How do you find the area of a parabola? (I just finished Algebra 2.)

Area of A Sector of An Ellipse [02/28/1998]

Finding the area of a sector of an ellipse, given the semiminor and major axes and the angles of the 2 vectors bounding the sector.

Area of a Segment from Arc and Chord Length [11/27/2000]

How do you find the area of a segment of a circle if you know only the arc length and chord length?

The Area of a Square Inscribed in a Circle [12/23/1995]

What is the area of a square inscribed in a circle whose circumference is 16 (pi).

Area of Inscribed Circle [12/01/1998]

Find the area of the circle inscribed in a triangle ABC using Heron's Law.

Area of Intersection of Two Circles [12/1/1995]

My teenage son asked me for the formula for the area of intersection of two arbitrary circles.

Area of Part of an Ellipse [04/07/2001]

Given an ellipse with a line bisecting it perpendicular to either the major or minor axis of the ellipse, what is the formula for the area of the ellipse either above or below that line?

Area of Union of Two Circles [6/10/1996]

If the effective length of a rope tied to a goat is L, and the goat can eat exactly half of the grass in a field, express L in terms of R.

Areas of N-Sided Regular Polygon and Circle [02/24/2005]

The area of an n-sided regular polygon approaches the area of a circle as n gets very large.

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