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WARRIOR [948]
3 years ago
9

Find the area of the following circle. (Round answer to the nearest whole number.) Circumference = 280 cm. (Hint: Find r from C

= 2πr (round r to tenths); then find area). 1) 89 2)560 3)1,989 4)6,246
Mathematics
2 answers:
Marrrta [24]3 years ago
4 0
Find r :
C=2πr
280=2(3.14)r
r=280/2(3.14)
r=44.6cm

find area :
A=πr²
A=3.14(44.6)²
A=6246 cm²

Answer : 4)6,246
pogonyaev3 years ago
4 0

Answer:

4)6,246

Step-by-step explanation:

First we will find the value of r.

The formula for circumference is C = 2πr:

280 = 2(3.14)r

280 = 6.28r

Divide each side by 6.28:

280/6.28 = 6.28r/6.28

44.6 ≈ r

The formula for the area of a circle is

A = πr²

Using our value for r, we have

A = 3.14(44.6)² = 6245.9624 ≈ 6246

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Answer:

\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: }  \frac{3\pi}{2}\text{ mi}

Step-by-step explanation:

The circumference of a circle with radius r is given by C=2\pi r. The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle \theta^{\circ} is equal to 2\pi r\cdot \frac{\theta}{360}.

Formulas at a glance:

  • Circumference of a circle with radius r: C=2\pi r
  • Length of an arc with central angle \theta^{\circ}: \ell_{arc}=2\pi r\cdot \frac{\theta}{360}

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting r=2 into our circumference formula, we get:

C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}

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\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}

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