Exploring Arc Length and Sector Area Formulas

This video tutorial covers the basic properties of circles, including circumference and area. It explains how to calculate the length of an arc and the area of a sector using specific formulas. The tutorial includes examples to demonstrate these calculations, using given measurements of angles and radii.

What is the formula to calculate the circumference of a circle?

• C = 2πr

• C = πr^2

• C = πd

• C = 2r

Tags

CCSS.7.G.B.4

How is the area of a circle calculated?

• A = r^2

• A = πd

• A = 2πr

• A = πr^2

Tags

CCSS.7.G.B.4

What do you need to calculate the length of an arc?

• Circumference and area

• Radius and diameter

• Radius and central angle

• Diameter and central angle

Tags

CCSS.HSG.C.B.5

What is the arc length formula?

• (θ/360) × 2πr

• θ × r

• πr^2

• 2πr

Tags

CCSS.HSG.C.B.5

How do you calculate the area of a sector?

• πr^2

• 2πr

• (θ/360) × πr^2

• θ × r^2

Tags

CCSS.HSG.C.B.5

If the diameter of a circle is 24 cm, what is the radius?

• 12 cm

• 48 cm

• 24 cm

• 6 cm

Tags

CCSS.7.G.B.4

For an angle of 120 degrees, what fraction of the circle's circumference does the arc represent?

• 1/6

• 1/2

• 1/4

• 1/3

Tags

CCSS.HSG.CO.A.1

CCSS.4.MD.C.5B

What is the length of the radius if the diameter is given as 24 cm?

• 12 cm

• 48 cm

• 24 cm

• 6 cm

Tags

CCSS.7.G.B.4

If a sector's central angle is 63 degrees, what fraction of the circle's area does the sector cover?

• 90/360

• 180/360

• 117/360

• 63/360

Tags

CCSS.HSG.CO.A.1

CCSS.4.MD.C.5B

How is the area of a sector with a central angle of 63 degrees and radius of 5 cm calculated?

• (63/360) × π × 5^2

• π × 5^2

• (63/360) × 2π × 5

• 2π × 5

Tags

CCSS.HSG.C.B.5