Circles - Area of Sector

Front

What is a circle?

Back

A circle is a shape consisting of all points in a plane that are at a given distance from a fixed point, called the center.

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula A = πr², where r is the radius.

Front

What is a sector of a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

How do you calculate the area of a sector?

Back

The area of a sector can be calculated using the formula A = (θ/360) × πr², where θ is the central angle in degrees.

Front

What is the relationship between the area of a sector and the area of the whole circle?

Back

The area of a sector is a fraction of the area of the whole circle, determined by the ratio of the central angle to 360 degrees.

Front

What is the unit of area for circles?

Back

The unit of area for circles is typically square units, such as cm², m², in², etc.

Front

If the radius of a circle is doubled, how does the area change?

Back

If the radius is doubled, the area increases by a factor of four, since area is proportional to the square of the radius.

Front

What is the area of a sector with a radius of 5 cm and a central angle of 90 degrees?

Back

The area of the sector is A = (90/360) × π(5)² = (1/4) × 25π = 6.25π cm².

Front

What is the area of a sector with a radius of 10 inches and a central angle of 180 degrees?

Back

The area of the sector is A = (180/360) × π(10)² = (1/2) × 100π = 50π in².

Front

What is the area of a sector with a radius of 7 m and a central angle of 60 degrees?

Back

The area of the sector is A = (60/360) × π(7)² = (1/6) × 49π = 8.17π m².