High School Level Questions on Circles and Spheres
from the Dr. Math Archives
High School Dr. Math Questions on Measurement
Below are some questions and answers from our archive of questions sent via e-mail by K12 students and teachers to Ask Dr. Math. You may also browse the entire high school level archive by category.
Back to High School Dr. Math Questions
Circles and Spheres
- Area of an Arc
- When you draw a circle and make a chord from one point to another, how would you find the area of that arc (formula)?
- Area, Angle of Chords of a Circle
- Calculate the angles PAB and POB, the area of the sector bounded by OP, OB and the minor arc PB.
- Area of Intersection of Two Circles
- My teenage son asked me for the formula for the area of intersection of two arbitrary circles.
- Area of Union of Two Circles
- 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.
- Circle Inscribed in Triangle
- What is the radius of a circle inscribed in a 3-4-5 right triangle?
- Circumference of a Circle Given Chord Length
- Given the length of a chord of a circle, is it possible to determine
- Cow Grazing in Circles
- A cow is tied to a 100 ft. rope (stay with me -- this _is_ interesting). His rope is tied to a pole in the center of a circle of radius 50 ft. This circle has a ten foot opening, out of which the cow can walk and graze. What's the area of grazing?
- Another Grazing Cow
- 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?
- Center of a Circle
- How can you find the center of a circle using a ruler and compass?
- Chord Length Formula
- What is the formula for the length of a chord given either the circle radius or the area of the resulting circle segment?
- Goat tied to a barn
- If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? Assume the goat is tied to a corner.
- Inscribed Angle, Circle Equation
- What's an inscribed angle? What's the equation for a circle with a
center at (8,-1) and a radius of 15?
- Isoperimetric Inequalities
- How can I prove that a circle has more area inside given its border length than any other shape?
- Radius, Center of Circle Given 3 Points
- What is an easy formula to calculate the center point and radius of a
circle given three points on the circumference?
- Sphere Formulas
- What are the formulas for area and volume of a sphere?
- Sphere in a Cube
- I have a cube of 200x200x200 and a sphere with a radius of 100 is inside it. I want to be able to put in x and y and using a formula get z.
- Sphere and Pyramid: Volume Equations
- Can you give me the formulas for the volume of a sphere and the volume of a pyramid?
- Triangle and Circle with same Center
- An equilateral triangle and a circle have the same center... find the length of the side of the triangle.
- Trigonometry and Geometry
- A right angle triangle is blocking a circle and is being blocked by
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