Area of a Sector and Arc Length

​11.1 Circumference & Arc Length/11.2 Areas of Circles and Sectors

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Multiple Choice

The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram.

Since the circumference of the circle can be represented by 2πr, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure? #14

• A = (2πr)(r)

• A = (2πr)(2r)

• $$A=\left(\frac{1}{2}\right)\left(2\pi r\right)\left(r\right)$$

• $$A=\left(\frac{1}{2}\right)\left(2\pi r\right)\left(r^2\right)$$ A =(2πr)(r2)

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Multiple Choice

What does "area" of a circle mean? #8

• The space a circle takes up

• The distance around a circle

• a line from one side of a circle to another

• a line from center of circle to side

Formulas you need to know

Multiple Choice

What is π ? (Best Choice)

Watch the video at the end of the question. #9

• The ratio of the circumference of any circle to its diameter.

• Exactly 3.14

• Exactly 3.1415

• Exactly 3.141593

The radius of a circle is.......

The measurement from the middle of the circle to the outside of the circle.

Multiple Choice

What does "circumference" mean? #1

• Space a circle takes up

• Distance around a circle

• Line from one side of a circle to another

• Line from center of circle to side

Multiple Choice

Does this picture show the diameter or radius of a circle? #2

• Diameter

• Radius

Multiple Choice

Does this picture show the diameter or radius of a circle? #3

• Diameter

• Radius

Multiple Choice

Find the circumference of a circle with a diameter of 11 millimeters. #4

• 34.6 mm

• 30 mm

• 25.3 mm

• 34.54 mm

Multiple Choice

What is the area of a circle with a diameter of 16 cm? #5

• 66 cm

• 200.96 cm

• 66.5 cm

• 10 m

Multiple Choice

Find the area of the circle. #6

• 56.52

• 254.34

• 1017.36

• 113.04

Multiple Choice

A circle has a radius of 6 inches. What is the area of the circle? (Best Choice) #10

• 3π or about 9.42 in²

• 6π or about 18.84 in²

• 12π or about 37.68 in²

• 36π or about 113.04 in²

Multiple Choice

Find the radius of a circle with an area of 125 in². Use the formula A=πr², where A is the area and r is the radius. Round your answer to the nearest tenth. #13

• 6.3 in

• 39.8 in

• 20 in

• 19.9

Multiple Choice

Alex has trained his puppy, Popper, to jump through a ring. According to Alex's measurements and calculations, the ring has a diameter of 3.5 feet. What is the ring's circumference (use 3.14 for pi)? #16

• 11.32 ft

• 12.25 ft

• 10.99 ft

• 8.75 ft

Arc Length (COPY NOTES)

Arc Length is the length of a portion of the circumference.

To find this we multiply the circumference by the fraction of the circle the arc subtends.

The fraction of the circle is determined by dividing the central angle by 360.

(NOTES)Example 1: Find length of minor arc AB.

Multiple Choice

Find the arc length of the bolded arc in the picture. (Use 3.14 for $$\pi$$  ) #20

$$S=\frac{\theta\cdot2\cdot\pi\cdot r}{360}$$  

• A

• B

• C

• D

Multiple Choice

Find the arc length. Round to the nearest tenth. DO NOT FORGET YOUR UNITS. #24

• 33.0 yd

• 16.5 ft

• 33.0 ft

• 17.8 yd

Fill in the Blanks

Multiple Choice

Find the length of the radius given the arc length of arc AB shown. Round your answer to the nearest tenth. #23

• 53.4 cm

• 154.3 cm

• 24.6 cm

• 12.8 cm

Multiple Choice

Given circle P, m $$\angle$$ RPT = 130°, and PT = 18 cm. Solve for area of the shaded sector. #34

• 367.57  cm²

• 207.23 cm²

• 324.08 cm²

• 182.67  cm²

Multiple Choice

Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch. #35

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Multiple Choice

Find the area of the shaded sector. Use 3.14 for pi. Round to the nearest tenth. #36

• 7.9 units ²

• 24.7 units²

• 10.6 units²

• 98.9 units²

Multiple Choice

Find the area of the shaded region to the nearest hundredth. #33

• 24.00 in²

• 12.57 in²

• 30.28 in²

• 17.72 in²

Multiple Choice

What is the exact circumference of the circle inscribed in the square? #32

• $$4.5\pi\ yd$$

• $$11\pi\ yd$$

• $$22\pi\ yd$$

• $$33\pi\ yd$$