Circles Unit Review

Front

What is the area of a sector of a circle?

Back

The area of a sector is given by the formula: \( \text{Area} = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is calculated using the formula: \( C = 2\pi r \) or \( C = \pi d \), where \( r \) is the radius and \( d \) is the diameter.

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is: \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.

Front

Convert the equation \( x^2 + y^2 - 22x - 20y - 4 = 0 \) to standard form.

Back

The standard form is: \( (x - 11)^2 + (y - 10)^2 = 225 \).

Front

What is the relationship between diameter and radius?

Back

The diameter is twice the length of the radius: \( d = 2r \).

Front

How do you find the area of a circle?

Back

The area of a circle is calculated using the formula: \( A = \pi r^2 \), where \( r \) is the radius.

Front

What is the formula for the area of a sector?

Back

The area of a sector is given by: \( \text{Area} = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the angle in degrees.

Front

What is the circumference of a circle with a diameter of 56 m?

Back

The circumference is: \( C = \pi d = \pi \times 56 \approx 175.8 \text{ m} \).

Front

What does the term 'circumference' refer to?

Back

Circumference refers to the measurement around the circle.

Front

What is the formula to convert from standard form to general form of a circle's equation?

Back

To convert from standard form \( (x - h)^2 + (y - k)^2 = r^2 \) to general form, expand and rearrange the equation.