Mathematics
Grade 10
15 min
Radius, diameter, circumference, and area of a circle
Radius, diameter, circumference, and area of a circle
What you'll learn
- Identify the radius, diameter, and circumference of a circle when given a visual representation with at least 80% accuracy.
- Solve for the diameter of a circle when given the radius, and solve for the radius when given the diameter, with 75% accuracy on a worksheet containing 4 problems.
- Apply the formula for circumference (C = πd or C = 2πr) to calculate the circumference of at least 3 out of 4 circles, given the radius or diameter.
- Apply the formula for area (A = πr²) to calculate the area of at least 3 out of 4 circles, given the radius.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the radius and diameter of a circle given the coordinates of its center and a point on the circle.
Determine the circumference of a circle using the distance formula to find its radius or diameter.
Calculate the area of a circle given the coordinates of its center and a point on the circle.
Find the radius, diameter, circumference, and area of a circle from its standard equation (x-h)² + (y-k)² = r².
Determine the center and radius of a circle given the coordinates of the endpoints of a diameter.
Apply the concepts of radius, diameter, circumference, and area to solve multi-step problems in the coordinate plane.
Ever wondered how GPS pinpoints your location using intersecting circles? 🛰️ Let's explore the powerful math that connects simple...
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Key Concepts & Vocabulary
TermDefinitionExample
CircleThe set of all points in a plane that are at a fixed distance (the radius) from a fixed point (the center).All points (x, y) that are exactly 5 units away from the center point C(2, 3).
Radius (r)The distance from the center of a circle to any point on the circle.The distance between the center C(1, 4) and a point P(4, 8) on the circle's edge.
Diameter (d)A line segment that passes through the center of a circle and has its endpoints on the circle. Its length is twice the radius (d = 2r).The length of the line segment connecting A(-2, 1) and B(4, 9), which passes through the center C(1, 5).
Circumference (C)The total distance (perimeter) around the outside of a circle.The perimeter of a circle with a radius of 10 units is 20π units.
Area (A)The amount of t...
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Core Formulas
Circumference Formula
C = 2πr or C = πd
Use this formula to find the distance around a circle. You need to know either the radius (r) or the diameter (d). Answers are often left in terms of π for precision.
Area Formula
A = πr²
Use this formula to find the space inside a circle. You must know the radius (r). If you are given the diameter, first divide it by 2 to find the radius.
Distance Formula (for Radius/Diameter)
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
In the coordinate plane, use this formula to find the length of the radius (distance from the center to a point on the circle) or the diameter (distance between two endpoints of a diameter).
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Sign Up Free to ContinueSample Practice Questions
Challenging
A circle has its center at C(2, -1) and passes through the point P(7, 11). What is the area of this circle?
A.13π sq units
B.26π sq units
C.169π sq units
D.144π sq units
Challenging
A circle has its center at (-4, 7) and is tangent to the y-axis. What is the circumference of the circle?
A.4π units
B.7π units
C.8π units
D.14π units
Challenging
A circle centered at (1, 1) has an area of 81π square units. Does the point P(10, 2) lie inside, on, or outside the circle?
A.Inside the circle
B.On the circle
C.Outside the circle
D.The point is the center of the circle
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Frequently asked questions
What grade level is "Radius, diameter, circumference, and area of a circle"?
Radius, diameter, circumference, and area of a circle is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Radius, diameter, circumference, and area of a circle?
You'll be able to: Identify the radius, diameter, and circumference of a circle when given a visual representation with at least 80% accuracy; Solve for the diameter of a circle when given the radius, and solve for the radius when given the….
Is "Radius, diameter, circumference, and area of a circle" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Radius, diameter, circumference, and area of a circle?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.