Question

In circle D with m/CDE = 144° and CD = 4, find the area of sector CDE.

Round to the nearest hundredth.

Answer 1

The area of a sector is given by the formula:

A = (θ/360°) x πr^2

where θ is the central angle of the sector and r is the radius of the circle.

In this case, we are given that CD = 4, so the radius of the circle is 2 (since CD is a diameter). We are also given that the central angle is 144°. Therefore, the area of sector CDE is:

A = (144/360) x π(2)^2

A = 0.4 x 4π

A = 1.57

Rounding to the nearest hundredth, we get:

A ≈ 1.57

Therefore, the area of sector CDE is approximately 1.57 square units.

Explanation:

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