Circle: Area and Circumference

Questions and Answers

A line that is inside the circle and touches the circle at two points

A line that runs through a circle and intersects two points on the circle's edge

A line that is outside of the circle and touches the circle at only one point (correct)

A line that forms a 90-degree angle with the radius of the circle

The distance from the center point to the edge of the circle

The distance between two points on the edge of the circle

The region inside the circle

The curved length around the circle (correct)

To distinguish them from other dimensions like arcs and chords (correct)

To find the area and circumference of other shapes

To calculate the perimeter of a square

To identify the center point of the circle

A section of the inside of the circle Signup and view all the answers

A circle angle Signup and view all the answers

Radius Signup and view all the answers

π(C/2π)^2 Signup and view all the answers

Divide the circumference by π Signup and view all the answers

2πr Signup and view all the answers

Divide 255.5 by π Signup and view all the answers

To find the area of the circle Signup and view all the answers

Study Notes

A circle is a closed arc around a center point, with a constant distance between the center and any point on the edge, known as the radius.
The diameter is the distance of a line segment that runs from one edge of the circle to the opposite edge, through the center point.
Other components of a circle include an arc (a portion of the circle's edge), a chord (a line segment connecting two points on the circle's edge), and a segment (a section of the inside of the circle).

A circle angle is formed by two radii with vertices at different locations on the circle's edge.
A tangent is a line that touches the circle at only one point, outside of the circle.
A secant is an extension of a chord, a line that runs through the circle and intersects two points on the circle's edge.

The area and circumference of a circle can be measured using various units (imperial or metric), but the units used must be units of length.
Common imperial units of length include inches, feet, and yards, while common metric units include millimeters, centimeters, and meters.

The area of a circle is the region or space measured inside the circle, or the total number of square units inside the circle.
The area of a circle can be calculated using the formula: A = πr^2, where π is approximately 3.14 and r is the radius.
The area of a semi-circle is half of the area of a circle.
The area of a circle can also be found using the diameter: A = π(d/2)^2.

There are two ways to find the circumference of a circle: using the diameter or the radius.
The circumference of a circle using the diameter is: C = πd.
The circumference of a circle using the radius is: C = 2πr.
Examples of finding the circumference of a circle include calculating the amount of siding needed for a circular pool or finding the circumference of a decorative circular plate.

To calculate the area of a circle using circumference, one must know the area and circumference formulas.
The area of a circle can be found using the circumference by: A = (C^2) / (4π).
This involves dividing the circumference by π, squaring the result, and multiplying by π.