Arc Length, Sector Area, and Equations of Circles

Front

What is the formula for the area of a sector of a circle?

Back

The area of a sector is given by the formula: A = (θ/360) * πr², where θ is the angle in degrees and r is the radius.

Front

How do you calculate the arc length of a circle?

Back

The arc length (s) can be calculated using the formula: s = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

The standard equation of a circle is (x - h)² + (y - k)² = r².

Front

What is the center of a circle given by the equation (x - 5)² + (y - 2)² = 16?

Back

The center of the circle is (5, 2).

Front

What is the radius of a circle given by the equation (x - 5)² + (y - 2)² = 16?

Back

The radius of the circle is 4, since r² = 16.

Front

How do you find the area of a circle?

Back

The area (A) of a circle is calculated using the formula: A = πr², where r is the radius.

Front

What is the relationship between the radius and diameter of a circle?

Back

The diameter (d) of a circle is twice the radius: d = 2r.

Front

What is the equation of a circle centered at (11, 0) with a radius of 9?

Back

The equation is (x - 11)² + y² = 81.

Front

What is the formula for the circumference of a circle?

Back

The circumference (C) of a circle is given by the formula: C = 2πr.

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply by (180/π).