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aleksandrvk [35]
3 years ago
7

Find the area of the circle that contains the sector described below. Round to the nearest tenth, if necessary.

Mathematics
1 answer:
Elis [28]3 years ago
6 0

Answer:

The area of the circle is 2520 cm²

Step-by-step explanation:

The area of an arc is given by the following formula:

arc area = pi*r²(angle/360)

In this case we have the area and the angle and we want to find r, so we have:

210 = pi*r²*(30/360)

210 = pi*r²*(1/12)

210*12 = pi*r²

pi*r² = 210*12

r² = 2520/pi

r = sqrt(2520/pi)

r = 28.3221

The area of the circle that has this arc is given by:

area = pi*r²

area = pi*(28.3221)² = 2520 cm²

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Luda [366]

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Step-by-step explanation:

Consider the below figure attached with this question.

According to Pythagoras Theorem:

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Use Pythagoras in triangle HKL

LH^2+KH^2=LK^2

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Taking square root on both sides.

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Use Pythagoras theorem in ΔKLI,

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Use Pythagoras theorem in ΔHKI,

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From (1) and (2) we get

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