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Naya [18.7K]
3 years ago
15

In a circle of radius 10 cm, a sector has an area of 40 (pi) sq. cm. What is the degree measure of the arc of the sector?

Mathematics
2 answers:
Rashid [163]3 years ago
6 0

Answer:

144°

Step-by-step explanation:

First, find the area of the circle, with the formula A = \pir²

Plug in 10 as the radius, and solve

A = \pir²

A = \pi(10²)

A = 100\pi

Using this, create a proportion that relates the area of the sector to the degree measure of the arc.

Let x represent the degree measure of the arc of the sector:

\frac{40\pi }{100\pi } = \frac{x}{360}

Cross multiply and solve for x:

100\pix = 14400\pi

x = 144

So, the degree measure of the sector arc is 144°

Semmy [17]3 years ago
3 0

Answer:

<h2><u>Solution</u><u> </u><u>:</u><u>-</u></h2>

We know that

Area = πr²

Area = 3.14 × (10)²

Area = 314/100 × 100

Area = 314 cm²

Now

40π/314 = x/360

40 × 3.14/314 = x/360

125.6/314 = x/360

0.4 = x/360

0.4 × 360 = x

144 = x

\\

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