Area of sector flashcardziz

Front

What is the formula for 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 angle in degrees and r is the radius of the circle.

Front

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

Back

To calculate the area of a shaded sector, use the formula A = (θ/360) * πr², substituting the values for θ (angle) and r (radius).

Front

What is the area of a sector with a radius of 10 inches and an angle of 90 degrees?

Back

Using the formula A = (θ/360) * πr², the area is A = (90/360) * π(10)² = (1/4) * 100π = 25π in².

Front

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

Back

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

Front

What is the area of a sector in terms of π if the radius is 8 and the angle is 45 degrees?

Back

Using the formula A = (θ/360) * πr², the area is A = (45/360) * π(8)² = (1/8) * 64π = 8π in².

Front

What does the term 'shaded sector' refer to in geometry?

Back

A shaded sector refers to a portion of a circle that is enclosed by two radii and the arc between them, often highlighted to indicate the area of interest.

Front

How do you convert the area of a sector from square inches to square centimeters?

Back

To convert from square inches to square centimeters, multiply the area in square inches by 6.4516, since 1 square inch is approximately 6.4516 square centimeters.

Front

What is the relationship between the angle of a sector and its area?

Back

The area of a sector is directly proportional to the angle; as the angle increases, the area of the sector also increases.

Front

What is the area of a sector with a radius of 5 inches and an angle of 120 degrees?

Back

Using the formula A = (θ/360) * πr², the area is A = (120/360) * π(5)² = (1/3) * 25π = (25/3)π in².

Front

What is the significance of leaving the area of a sector in terms of π?

Back

Leaving the area in terms of π provides an exact value rather than a decimal approximation, which can be useful in mathematical proofs and further calculations.