U6 D6 Arc Length, Area of Sectors

Front

What is the formula for arc length when the angle is in radians?

Back

Arc Length = r * θ, where r is the radius and θ is the angle in radians.

Front

How do you convert degrees to radians?

Back

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

Front

What is the relationship between the radius and the arc length in a circle?

Back

The arc length is directly proportional to the radius and the angle in radians.

Front

If the diameter of a circle is 10 cm, what is the radius?

Back

The radius is 5 cm.

Front

What is the area of a sector of a circle?

Back

Area of Sector = (θ/2) * r², where θ is in radians.

Front

How do you find the area of a sector when the angle is given in degrees?

Back

Convert the angle to radians first, then use the formula Area of Sector = (θ/2) * r².

Front

What is the formula for finding the area of a sector when the angle is in degrees?

Back

Area of Sector = (θ/360) * π * r².

Front

What is the arc length of a circle with a radius of 6 inches and a central angle of 100°?

Back

First convert 100° to radians, then use the arc length formula.

Front

What is the significance of the central angle in relation to arc length?

Back

The central angle determines the size of the arc length; larger angles result in longer arcs.

Front

How do you find the radian measure of an angle if you know the arc length and radius?

Back

Use the formula θ = Arc Length / r.