Circle Practice 2 pt 1 : Area of sector

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) * π * r², where θ is the central angle in degrees and r is the radius.

Front

What does the term 'central angle' refer to in a circle?

Back

The central angle is the angle formed at the center of the circle by two radii.

Front

How do you calculate the radius if you know the area of the sector and the central angle?

Back

Rearrange the area formula: r = √(Area * 360 / (π * θ)).

Front

What is the value of π (pi) commonly approximated as?

Back

π is commonly approximated as 3.14.

Front

If the radius of a circle is 7 cm, what is the area of the entire circle?

Back

Area = π * r² = 3.14 * (7)² = 153.86 cm².

Front

What is the relationship between the radius and the area of a sector?

Back

The area of a sector increases with the square of the radius.

Front

How do you convert degrees to radians for calculations involving circles?

Back

Radians = Degrees * (π/180).

Front

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

Back

Area = (90/360) * π * (5)² = 19.63 square inches.

Front

What is the significance of rounding in area calculations?

Back

Rounding provides a more manageable number for practical applications, but it can affect precision.

Front

If a sector has an area of 24.7 square units and a central angle of 120 degrees, what is the radius?

Back

r = √(Area * 360 / (π * θ)) = √(24.7 * 360 / (3.14 * 120)) ≈ 4.0 units.