Illustrative Mathematics - Geometry - Unit 7 - Lesson 11

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Last updated about 1 year ago

14 Questions

Here is a central angle that measures 1.5 radians.
 Select all true statements.

The radius is 1.5 times longer than the length of the arc defined by the angle.

The area of the whole circle is 1.5 times the area of the slice.

The circumference of the whole circle is 1.5 times the length of the arc formed by the angle.

The ratio of arc length to radius is 1.5.

The length of the arc defined by the angle is 1.5 times longer than the radius.

The ratio of radius to arc length is 1.5.

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

Match each arc length l and radius r with the measure of the central angle of the arc in radians.

		\frac{\pi}{5} radians
		\frac{2}{3} radians
		0.75 radians
		\frac{\pi}{4} radians
		0.8 radians

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

Han thinks that since the arc length in circle A is longer, its central angle is larger.
 Do you agree with Han? Show or explain your reasoning.

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

10.

11.

12.

A circle has radius 8 units, and a central angle is drawn in. The length of the arc defined by the central angle is 4\pi units. 

Find the area of the sector outlined by this arc.

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

13.

Clare is trying to explain how to find the area of a sector of a circle. She says, “First, you find the area of the whole circle. Then, you divide by the radius.“

 Do you agree with Clare? Explain or show your reasoning.

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

14.

Line BD is tangent to a circle with diameter AB.
 List 2 right angles.

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

This lesson is from Illustrative Mathematics. Geometry, Unit 7, Lesson 11. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/7/11/index.html ; accessed 29/July/2021.

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