MA.912.GR.6.4: Arc Length and Area of a Sector

A circle has radius 8 ft and a central angle of 45°. What is the arc length in terms of π?

• 2π ft

• 4π ft

• π ft

• (2π)/3 ft

Tags

CCSS.HSG.C.B.5

A circle of radius 10.8 in has a small sector with central angles 81°. What is the area of the smaller sector to the nearest tenth?

• 55.0 in^2

• 59.0 in^2

• 82.4 in^2

• 57.0 in^2

Tags

CCSS.HSG.C.B.5

The circle has a radius of 10.8. What is the area of the larger sector to the nearest tenth?

• 226.0 in^2

• 283.98 in^2

• 205.0 in^2

• 213.0 in^2

Tags

CCSS.HSG.C.B.5

Which of the following is the formula for arc length?

• arc length = measure of arc/360 times 2πr

• Arc length = 360/ measure of arc times 2πr

• Arc length= 2πr/360 times measure of arc

• 2πr

Tags

CCSS.HSG.C.B.5

A sector of a circle has area 100 in^2 and central angle 30°. What equation in r solves for the circle's radius?

• (πr)(30/360) = 100

• (1/2)r(π/6) = 100

Tags

CCSS.HSG.C.B.5

In an error analysis, a student finds sector area using n/360 = 115/255 with n labeled as area. Which statement best identifies the structural error?

• Using radians instead of degrees in setup

• Mismatched angle and area units in proportion

• Angles placed on opposite sides of the proportion

• Assuming a semicircle instead of full circle

Tags

CCSS.HSG.C.B.5

For the same error analysis scenario, what is the correct answer?

• 81.46 feet squared

• 79.42 feet squared

• 14 feet squared

• 67.5 feet squared

Tags

CCSS.HSG.C.B.5

A circle has radius r. Doubling the central angle of a sector while keeping r fixed will do what to the arc length and sector area?

• Length doubles, area quadruples

• Both double

• Both quadruple

• Length halves, area doubles

Tags

CCSS.HSG.C.B.5

A 60° sector has arc length 12 cm. What is the circle radius?

• 8.5 cm

• 9.5 cm

• 10.5 cm

• 11.5 cm

Tags

CCSS.HSG.C.B.5

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47
• 74
• 94
• 123

Tags

CCSS.HSG.C.B.5