Geometry | Unit 7 | Lesson 11: A New Way to Measure Angles | Practice Problems

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

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

• The ratio of arc length to radius is 1.5.

• The ratio of radius to arc length is 1.5.

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

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

Match each arc length \(\ell\) and radius \(r\) with the measure of the central angle of the arc in radians.

• E: \(r=5, \ell=\pi\)

• D: \(r=4, \ell=3\)

• C: \(r=3.5, \ell=2.8\)

• B: \(r=3, \ell=2\)

• A: \(r=2,\ell=\frac{\pi}{2}\)

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.

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Circle B is a dilation of circle A.

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Priya and Noah are riding different size Ferris wheels at a carnival. They started at the same time. The highlighted arcs show how far they have traveled.

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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.

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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.

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

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