Illustrative Mathematics - Geometry - Unit 7 - Lesson 11

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 length of the arc defined by the angle is 1.5 times longer than the radius.
• The ratio of arc length to radius is 1.5.
• The ratio of radius to arc length is 1.5.
• The area of the whole circle is 1.5 times the area of the slice.

Tags

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.

Evaluate responses using AI:

OFF

Tags

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

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.

Evaluate responses using AI:

OFF

Tags

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

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.

Evaluate responses using AI:

OFF

Tags

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1

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

Evaluate responses using AI:

OFF

Tags

A.SSE.1.a

G.C.5

A.SSE.1.b

G.C.1