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I am Lyosha [343]
3 years ago
14

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. The central angle formed by the peach co

bbler is 105 degrees. The central angle formed by the pasta is 203 degrees. What is the approximate length of the arc of the section containing the peas? A. 3 inches B. 21 inches C. 16 inches D. 5 inches
Mathematics
1 answer:
Vsevolod [243]3 years ago
6 0

Answer:

D. 5 inches

Step-by-step explanation:

Given:

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.

That means complete angle having 360° is divided into 3 section.

The central angle formed by the peach cobbler is 105 degrees.

The central angle formed by the pasta is 203 degrees.

<u>Question asked:</u>

What is the approximate length of the arc of the section containing the peas?

<u>Solution:</u>

The central angle formed by the peas = 360° - 105° - 203°

                                                                = 52°

Ridius,r=\frac{Dameter}{2} =\frac{12}{2} =6\ inches

As we know:

Length\ of\ arc=2\pi r\times\frac{\Theta }{360}

                        =2\times\frac{22}{7} \times6\times\frac{52}{360} \\ \\ =\frac{13728}{2520} \\ \\ =5.44\ inches

Therefore, the approximate length of the arc of the section containing the peas are 5 inches.

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