Sector Area, Segment 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: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

Define the area of a segment of a circle.

Back

The area of a segment is the area of the sector minus the area of the triangle formed by the two radii and the chord.

Front

What is the equation of a circle centered at the origin with radius r?

Back

The equation is given by: \( x^2 + y^2 = r^2 \).

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 relationship between the radius and diameter of a circle?

Back

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

Front

What is the formula for the circumference of a circle?

Back

The circumference is given by the formula: \( C = 2\pi r \).

Front

How do you calculate the area of a segment given the radius and angle?

Back

The area of a segment can be calculated using the formula: \( A = \frac{1}{2} r^2 (\theta - \sin(\theta)) \), where \( \theta \) is in radians.

Front

What is the equation of a circle centered at (h, k) with radius r?

Back

The equation is given by: \( (x - h)^2 + (y - k)^2 = r^2 \).

Front

What is the area of a sector with a radius of 5 cm and an angle of 60 degrees?

Back

The area is \( A = \frac{60}{360} \times \pi (5^2) = \frac{1}{6} \times 25\pi = \frac{25\pi}{6} \) cm².

Front

What is the area of a circle with a radius of 3 cm?

Back

The area is \( A = \pi (3^2) = 9\pi \) cm².