Calculating Arc Length and Sector Area in Circles

What is the formula to calculate arc length when the angle is in radians?

• s = r / theta

• s = 2 * pi * r

• s = theta * r

• s = theta / r

Tags

CCSS.HSG.C.B.5

If a circle has a radius of 12 feet and an angle of 5 radians, what is the arc length?

• 30 feet

• 17 feet

• 60 feet

• 24 feet

Tags

CCSS.HSG.C.B.5

How do you convert an angle from degrees to radians for arc length calculation?

• Multiply by pi / 180

• Multiply by 180 / pi

• Divide by pi / 180

• Divide by 180 / pi

Tags

CCSS.HSF.TF.A.1

What is the arc length if the radius is 8 cm and the angle is 150 degrees?

• 25.132 cm

• 10.472 cm

• 20.944 cm

• 15.708 cm

Tags

CCSS.HSG.C.B.5

What is the relationship between the arc length formula in radians and the formula in degrees?

• They are completely different.

• The radians formula is derived from the degrees formula.

• They are interchangeable without conversion.

• The degrees formula is derived from the radians formula.

Tags

CCSS.HSG.C.B.5

What formula is used to calculate the area of a sector when the angle is in radians?

• Area = 2 * pi * r

• Area = pi * r^2

• Area = 1/2 * theta * r^2

• Area = theta * r^2

Tags

CCSS.HSG.C.B.5

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

• Area = theta / 360 * pi * r^2

• Area = theta / 360 * 2 * pi * r

• Area = theta * pi * r^2

• Area = 1/2 * theta / 360 * pi * r^2

Tags

CCSS.HSG.C.B.5

If a sector of a circle has a 90-degree angle and a radius of 10 cm, what is the area of the sector?

• 100 pi cm^2

• 25 pi cm^2

• 50 pi cm^2

• 75 pi cm^2

Tags

CCSS.HSG.C.B.5

If the radius of a circle is 5 feet and the sector angle is 60 degrees, what is the area of the sector?

• 25/6 pi square feet

• 10/3 pi square feet

• 15/4 pi square feet

• 5/2 pi square feet

Tags

CCSS.HSG.C.B.5

For an angle of 2 radians and a radius of 8 cm, what is the area of the sector?

• 16 square cm

• 32 square cm

• 128 square cm

• 64 square cm

Tags

CCSS.HSG.C.B.5