NB _ Circles: Sector Area - Arc Length

Arc Length & Area of a Sector

Objective: Use proportional reasoning to find arc length and area of a sector

Arc Length

Ex 1: Find the length of the minor arc

If I want to find the area of an part of a circle, how would I do it?

Area of a Sector

Multiple Choice

What is the radius of a circle that has a central angle of 230 degrees and an arc length of 60 miles.

• 6.10 miles

• 74.95 miles

• 29.89 miles

• 14.95 miles

Ex 1:

Ex. 2:

Multiple Choice

Find the length of the bold arc. Leave $$\pi$$   in your answer.

• 5688π ft

• 15.8π ft

• 150.4π ft

• 54,150 ft

Multiple Choice

Find the length of the arc.

• 31.42cm

• 15.71cm

• 282.74cm

• 23.56cm

Multiple Choice

What is the area of the shaded sector? Round your answer to the nearest hundredth. Use 3.14 for π

• 9.64

• 163.85

• 743.61

• 43.74

Example

Multiple Choice

Find the sector area of the wedge.

• 10.99 $$cm^2$$

• 76.96 $$cm^2$$

• 87.96 $$cm^2$$

• 615.75 $$cm^2$$

Multiple Choice

In the diagram, if the radius of the circle is 25 units, what is the length of arc AB?

• 
  $$\frac{\text{2}}{\text{5}}\pi$$

• $$5\pi$$

• $$10\pi$$

• $$50\pi$$

Multiple Choice

Find the area of the shaded sector of the circle. Leave answer in terms of π

• 5.83π

• 43.75π

• 68.75π

• 4.58π

Multiple Choice

What is the area of the shaded region? Round to the nearest hundredth.

• 4.71

• 339.29

• 9.42

• 113.10

Multiple Choice

Given circle P, the white arc has an angle measure = 130°, and PT = 18 cm.
Solve for area of the shaded sector.

• 20.42 cm²

• 650.31 cm²

• 367.57 cm²

• 36.13 cm²

Multiple Choice

If the circle inscribed in square ABCD has a radius of r, what is the size of the shaded area in terms of r?

• $$r^2-\pi r^2$$

• $$2r-\pi r^2$$

• $$\frac{r}{2}-\frac{\pi r^2}{4}$$

• $$r^2-\frac{\pi r^2}{4}$$

Multiple Choice

Find the area of the shaded region.

• 125.7 cm²

• 40 cm²

• 103.7 cm²

• 33 cm²

Multiple Choice

If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?

• 161.97 mm²

• 155.37 mm²

• 148.13 mm²

• 142.74 mm²

Multiple Choice

Find the area of the shaded region. Along the top is 9 cm. (Hint: Find 3 separate areas -- whole thing and then 2 non shaded pieces-- then subtract non shaded from the whole thing)

• 162 cm ²

• 63.61 cm ²

• 98.4 cm ²

• 34.76 cm ²