Chapter 5 - Circles & Cylinders Flashcards

Questions and Answers

What is the formula for circumference?

Circumference = $2 imes ext{Pie} imes r$ (correct)

Circumference = $rac{Area}{Diameter}$

Circumference = $ ext{Pie} imes d$ (correct)

Circumference = $ ext{Pie} imes r^2$

What is the formula for the area of a circle?

A = $ ext{Pie} imes r^2$

A central angle's vertex lies on the circle.

False

What is the relationship between an inscribed angle and the arc it intercepts?

An inscribed angle is equal to half of the arc it intercepts. Signup and view all the answers

All vertices of an inscribed triangle must lie on the circle.

True Signup and view all the answers

What must be true if one side of an inscribed triangle is a diameter?

The triangle must be a right triangle. Signup and view all the answers

What is the formula for the volume of a cylinder?

V = $ ext{Pie} imes r^2 imes h$ Signup and view all the answers

The Area of a Sector is calculated as the degree of the angle divided by ____ times the area of the circle.

360 Signup and view all the answers

If the angle of a sector is 60 degrees, what fraction of the area of the circle does it represent?

60/360 Signup and view all the answers

Study Notes

Circle Measurements

Circumference formula: ( C = \pi \times d = 2 \times \pi \times r )
Area of a circle formula: ( A = \pi \times r^2 )

Angles in a Circle

A central angle has its vertex at the circle's center.
An inscribed angle has its vertex on the circle's circumference.
An inscribed angle is half the measure of the arc it intercepts; for example, if an arc measures 60 degrees, the inscribed angle measures 30 degrees.

Inscribed Triangles

A triangle inscribed in a circle has all its vertices on the circle.
If one side of the inscribed triangle is a diameter, the triangle is a right triangle.
Any right triangle inscribed in a circle will have the circle's diameter as one of its sides, bisecting the circle.

Cylinders and Their Volume

Volume of a cylinder formula: ( V = \pi \times r^2 \times h )
Variables: ( V ) = volume, ( r ) = radius, ( h ) = height.

Area of a Sector

Area of a sector formula: ( \text{Area of Sector} = \frac{\text{degree}}{360} \times \text{Area of Circle} )
For a 60-degree angle, it represents ( \frac{60}{360} ) of the circle's area.

Description

Explore the key concepts of circles and cylinders with these flashcards. This quiz covers essential definitions such as radius, diameter, circumference, area, and the difference between inscribed and central angles. Perfect for reinforcing your understanding of circle geometry.