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FAQs with keywords: circular - 8 items found
Analytic Geometry: Cylindrical Coordinates (Ask Dr. Math FAQ)
A discussion of cylindrical coordinates and their common uses.

Analytic Geometry: Spherical Coordinates (Ask Dr. Math FAQ)
A discussion of spherical coordinates and their common uses.

Cone Formulas (Ask Dr. Math FAQ)
Formulas for finding the height, surface area, and volume of a cone, right circular cone, or frustum of a cone.

Cylinder Formulas (Ask Dr. Math FAQ)
Formulas for finding the surface area and volume of a general cylinder and a right circular cylinder.

Ellipsoid, Torus, Spherical Polygon Formulas (Ask Dr. Math FAQ)
Formulas for finding the surface area and/or volume of an ellipsoid, a prolate spheroid, an oblate spheroid, a circular or ring torus, and a spherical polygon.

Geometric Formulas (Ask Dr. Math FAQ)
Formulas for two-dimensional figures: triangle (equilateral, isosceles, right, scalene); quadrilateral (general, square, rectangle, parallelogram, rhombus, trapezoid, kite, cyclic and cyclic-inscriptable); regular polygon; circle (arc, segment, sector); ellipse; parabolic segment; and three-dimensional figures: rectangular parallelepiped (cube); prism; pyramid (square pyramid, frustum); regular polyhedron (tetrahedron, cube, octahedron, dodecahedron, icosahedron); cylinder (right circular); cone (right circular, frustum); sphere (sector, cap, segment, zone, lune); ellipsoid; circular torus; spherical polygon. Includes Defining Geometric Figures.

Grazing Animals
A cow/goat/donkey is tethered to a barn in or a fence around a field... how long should the rope be so that she can eat half the grass?

Sphere Formulas (Ask Dr. Math FAQ)
Formulas for finding the surface area and volume of a sphere, sphere sector, spherical cap, and segment, zone, and lune of a sphere.


Items with keywords: circular - 211 items found, showing 1 to 50
3-D Shape That Can Be a Circle, Square, or Triangle in 2-D [09/08/2006]
Is there a shape that can fill and pass through a circular hole, a square hole, and a triangular hole?

About Hyperbolas [8/7/1996]
Find the graph and the equation of a hyperbola.

Acceleration around a Corner [09/17/2005]
What is the formula to find out the acceleration of an object going around a corner?

Adjusting Gear Sizes [07/14/2000]
Some material is to be cut into 4" pieces that are 1/8" apart by passing it through two sets of vertical rollers connected by a gear. What diameter of the second bottom roller will give the right separation?

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 of Flight [11/27/1997]
A fly is sitting at 12 o'clock on a frictionless clock. He takes a step to one side and begins to slide down the clock...

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?

Applied Max/Min Problems [2/11/1996]
Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius r.

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.

Area of an Ellipse without using Calculus [11/28/1997]
How do you find the area of an oval without using calculus?

Area of Intersection of Two Circular Segments [04/20/2007]
Given a circle of radius r and center c, suppose two intersecting chords AB and CD (intersecting in P) form two circular segments. How do I compute the area of the intersection of the two circular segments?

The Area of Triangles using Hero's Formula [12/13/1995]
If a person gave three dimensions of a triangle (in feet) and noted the base dimension, without knowing the angles because the other two lines would have to intersect someplace, is there a formula that could calculate the area?

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.

Arranging Rose Bushes [9/13/1995]
A gardener laying out a rosebed found she could plant 7 rose bushes in such a way that they formed 6 straight lines with 3 rose bushes in each line. How was this possible?

Average Radial Distance of Points within a Circle [03/26/2003]
I'm trying to determine the average value of a circular/radial gradient that is at full value (white, call it 100% brightness) in the center, and drops in a linear fashion to zero (black, call it 0% brightness) at the radius.

Beads on a Bracelet [05/04/1997]
How many different arrangements of 3 red and 3 blue beads on a bracelet are there?

Breaking the Sound Barrier [10/21/1997]
I am trying to find a way to incorporate breaking the sound barrier into a math lesson for my third grade class.

Building a Circular Horse Pen [06/16/2002]
My Dad and I are building a round pen for our horse. We have 16 16ft. panels and a 10 ft. gate and a 4ft. gate. (270 ft. total) We want to use a radius and mark the places to dig holes for each post that will support the panels, but we don't know how long the radius should be. Can you help?

Calculating the Diameter of a Carpet Roll [9/24/1995]
How do you calculate the diameter of a carpet roll when you have the length and the thickness?

Calculus: Rate of Change in Volume [07/27/1997]
The radius of a right circular cylinder is decreasing at the rate of 4 feet per minute, while the height is increasing at the rate of 2 feet per minute. Find the rate of change in the volume when the radius is 2 feet and the height is 6 feet.

Cantor, Peano, Natural Numbers, and Infinity [03/19/1998]
A conversation on transfinite numbers and contradictions the questioner believes exist in Cantor's paper introducing the diagonal method.

Can Two Curves Be Parallel? [12/19/2007]
Straight lines are parallel if they are equally distant and never intersect. Can the graphs of quadratic or cubic equations be considered parallel if they are equally distant and never intersect?

Cauchy Principal Value [05/23/2000]
Can you tell me what the Cauchy Principal Value is?

Centering Circles [10/05/2002]
Two metal disks need to be centered on each other, but the circle with the larger diameter has the center cut out. How can you center them by knowing the diameters?

Center of Mass of a Semicircle [06/14/1999]
Is there a standard formula I can use to know where the center of mass of a semicircle is?

Centripetal Acceleration [05/05/1997]
When a vehicle is going around a curve, are the forces balanced?

Circle Revolutions [07/02/2002]
Our teacher gave everyone a CD, and told us to look at the spin of the smaller inner circle and of the large outer circle. We have concluded that they both make a revolution in the same amount of time, but they moving at different speeds. Is that possible?

Circles on the Surface of a Sphere [08/11/1999]
How can I convert the equation of a circle on a unit sphere in the (X,Y,Z) coordinate system into a function that is defined in terms of spherical coordinates theta and phi?

Circular Field, Cow, and Length of Rope [9/11/1996]
A cow is tied with a rope to the edge of a circular field 10 ft. in diameter. How long must the rope be so the cow can graze half the field?

Circular Functions [01/27/2001]
How do you define circular functions? Can you give me an example?

A Circular Massacre [09/25/1998]
Ten thousand sailors are arranged in a circle; starting with the first one, every other sailor is pushed overboard ....

Circular Motion [01/27/2001]
Two problems: An electric hoist is being used to lift a piece of equipment... A car is moving at a rate of 50 miles per hour and the diameter of its wheels is 2.5 feet...

Circular Motion and Acceleration [12/03/1999]
How can an object experiencing circular motion always be accelerating toward the center if the distance from the center is constant?

Circular Motion in a Cassette Player [11/7/1995]
The tape in a cassette player passes over the head at 5 cm per second onto a takeup spool of 5 cm diameter. The tape is 0.01 cm thick. Find an expression for the angular speed of the takeup spool at time t seconds. What modelling assumptions do you make?

Circular Permutations [08/07/2005]
With four card players at a round table, how many different seating arrangements exist from a sequential point of view?

Circumference of a Tube [10/11/2001]
What effect does the thickness of a tube have on the circumference when it's formed into a circle?

Civil Engineering and Math [02/25/1997]
What forms of math or physics do civil engineers commonly use?

Classical Geometry [04/16/2002]
Let ABC be a triangle with sides a, b, c. Let h be the perpendicular from A to a, and m the median from A to the midpoint of a. Construct the triangle using only ruler and compass if you know A, h, m.

Coin With 11 Sides and a Constant Diameter [10/20/2007]
I was told that one of the reasons why a Canadian Loonie coin is 11-sided is that it rolls better than a 10-sided coin. Why is that?

Collision of Two Circular Objects [02/02/2002]
If I have two coins moving across a frictionless surface, knowing their velocity and angles, how can I find the angle of each object after they collide?

Comparing Size of Infinite Subset to Parent Infinity Subset [12/16/2001]
If one considers the single, original set of all positive integers the "physiological" state and wants to compare the size of the positive even integers to the total positive integers, doesn't the splitting out of the evens into a separate subset constitute an experimental artifact that doesn't accurately reflect the original state?

Complex Integrals and the Residue Theorem [12/18/2000]
How can I calculate the integral over C of (z^2/((z-1)^2*(z+1)))dz, where C is the circle C = {z| |z - 2i| = 2}? Can I use the Taylor Series?

Cone Symmetry [7/17/1996]
Why does a circular cone have infinite lines of symmetry?

Cone Volume [04/19/1999]
A right circular cone is circumscribed about a sphere of radius R cm. Find the ratio of the altitude to the base radius of the cone of largest possible volume.

Conical Drinking Cup [06/20/1997]
A conical drinking cup is made from a circular piece of paper of radius r by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup.

Constructing a Line to Divide Area of a Triangle in Half [05/13/1998]
Cutting a triangle into two pieces of equal area by drawing a a line parallel to one of the sides.

Container Height and Volume [08/01/1997]
A container's height is increased by 4 cm, and the length and width remain the same. If this change increased the volume by 12 percent, what was the original height of the container?

Coordinate Geometry - Goat in a Circular Field [8/22/1996]
A goat is tethered by a rope of length L to a point on the circumference of a circular field of radius R. Find L in terms of R if the goat can graze exactly half the area of the field.

Cow Grazing Half the Circle: Newton-Raphson Method [01/18/1998]
Assume a perfect circle filled with grass and a cow tied with a rope to the fence around it...

Curved Tracks, Driven Side by Side ... at Different Speeds? [03/14/2014]
An adult wonders whether road curvature accounts for the different speeds reported by her cruise control and by the highway patrolman who pulled her over. After distinguishing between speed and angular velocity, Doctor Carter calculates gravitational accelerations to model the event and check the plausibility of the data.

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