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Questions and Answers
What is the formula for circumference?
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?
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.
A central angle's vertex lies on the circle.
False (B)
What is the relationship between an inscribed angle and the arc it intercepts?
What is the relationship between an inscribed angle and the arc it intercepts?
All vertices of an inscribed triangle must lie on the circle.
All vertices of an inscribed triangle must lie on the circle.
What must be true if one side of an inscribed triangle is a diameter?
What must be true if one side of an inscribed triangle is a diameter?
What is the formula for the volume of a cylinder?
What is the formula for the volume of a cylinder?
The Area of a Sector is calculated as the degree of the angle divided by ____ times the area of the circle.
The Area of a Sector is calculated as the degree of the angle divided by ____ times the area of the circle.
If the angle of a sector is 60 degrees, what fraction of the area of the circle does it represent?
If the angle of a sector is 60 degrees, what fraction of the area of the circle does it represent?
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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.
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