Common Core Standard HSG-C.B.5 Questions

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

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Grade 10 Circles CCSS: HSG-C.B.5

A circle with a diameter of 20 inches has an arc of 45 degrees. What are the arc length and sector area of that arc? Round to the hundredth place.

Grade 10 Circles CCSS: HSG-C.B.5

Given a circle of radius 4, what is the length of an arc which subtends an angle of [math](2 pi)/5 ?[/math] Use [math]pi = 3.14[/math] and round answer to two decimal places.

5.24
20.10
0.09
5.02

Grade 10 Circles CCSS: HSG-C.B.5

Given a circle with radius 5, what is the area of a sector bounded by two radii which make an angle of 2.35 radian, rounded to two decimals?

5.88 units squared
29.38 units squared
0.26 units squared
78.54 units squared

Grade 9 Circles CCSS: HSG-C.B.5

Find the arc length of an arc with measure 140 degrees in a circle with radius 3 in. Round to the nearest tenth.

Grade 9 Circles CCSS: HSG-C.B.5

Adam has a circular pizza with a radius of 20 cm. The arc length of the crust of the first slice he takes is 17.5 cm. What is the area of Adam's slice of pizza? Round the answer to the nearest integer, if necessary.

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