Exploring Circumference and Arc Length of Sectors

This video tutorial covers the concepts of circumference and arc length of a circle. It begins with an introduction to the formula for circumference, followed by examples of calculating circumference using given radius and area. The tutorial then explains arc length as a portion of the circumference and provides examples of calculating arc length in various scenarios. Advanced techniques for arc length calculation are also discussed.

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

• Both A and B

• C = πr^2

• C = 2πr

• C = πd

Tags

CCSS.7.G.B.4

If the radius of a circle is 7 units, what is its circumference?

• 28π units

• 22 units

• 44 units

• 14π units

Tags

CCSS.7.G.B.4

What is the area of a circle if its circumference is 40π units?

• 400π square units

• 200π square units

• 40π square units

• 800π square units

Tags

CCSS.7.G.B.4

If a circle's area is 16π square units, what is its circumference?

• 16π units

• 32π units

• 8π units

• 4π units

Tags

CCSS.7.G.B.4

How is the arc length of a circle's sector calculated?

• s = θ/360 × 2πr

• s = rθ

• Both A and B

• s = θ/360 × πd

Tags

CCSS.HSG.C.B.5

For a sector with a 120-degree central angle in a circle of 9 units radius, what is the arc length?

• 3π units

• 18π units

• 12π units

• 6π units

Tags

CCSS.HSG.C.B.5

How does the formula for arc length relate to the formula for the area of a sector?

• Both involve the radius squared

• Both are independent of the circle's size

• Both use the central angle over 360

• Both multiply by π

Tags

CCSS.HSG.C.B.5

What is the perimeter of Pac-Man if his mouth, with a radius of 5 units, is open at an angle of 50 degrees?

• 10 units

• 50 units

• 27.1 units

• 37.1 units

Tags

CCSS.HSG.C.B.5

If the arc length of a shaded section is 15π and the central angle is 60 degrees, what is the circle's diameter?

• 45 units

• 60 units

• 90 units

• 30 units

Tags

CCSS.HSG.C.B.5

What is the correct way to find the radius if you know the arc length and the central angle?

• All of the above

• Use the circumference formula in reverse

• Divide arc length by π and then solve for the radius

• Multiply arc length by 360/θ

Tags

CCSS.HSG.C.B.5