+0

# help!

0
68
3
+862

Find the area of the segment of the circle :)

May 10, 2021

#1
+32833
+1

Calculate the entire area of the 60 degree arc then subtract the area of the equilateral triangle

pi r^2  *  60 / 360   = 6 pi

Area of eqil triangle    sqrt 3/ 4  * 6^2

6 pi   -   sqrt 3  / 4   * 36 = 3.261 cm2

May 10, 2021
#2
+862
0

Thank you!

AnimalMaster  May 10, 2021
#3
+498
+1

The area of a sector of a circle given the radius (r) and the angle (a) is $\frac{a}{360} \cdot r^2 \cdot \pi$

Here, the angle is $60$ and the radius is $6$ so we have $\frac{60}{360} \cdot 6^2 \pi= \frac{1}{6} \cdot 36 \pi = 6 \pi.$

The area of the equilateral triangle: We first must know the height and width, which is 6, but we do not know the height(I am assuming we do not know the formula for the area of an equilateral triangle.) Let the height be $h.$ We have $(\frac{6}{2})^2 + h^2 = 6^2 \Rightarrow 9 + h^2 = 36 \Rightarrow h^2 = 27 = 3 \sqrt{3}.$

The height is $3\sqrt{3},$ so the area is $\frac{1}{2} \cdot 3\sqrt{3} \cdot 6 = 9 \sqrt{3}.$

The answer is the sector - equilateral triangle = $6 \pi - 9 \sqrt{3}.$

May 10, 2021
The text passage contains a mathematical question about finding the area of a segment of a circle, and multiple answers are provided in the subsequent comments.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
+0

# help!

0
68
3
+862

Find the area of the segment of the circle :)

May 10, 2021

#1
+32833
+1

Calculate the entire area of the 60 degree arc then subtract the area of the equilateral triangle

pi r^2  *  60 / 360   = 6 pi

Area of eqil triangle    sqrt 3/ 4  * 6^2

6 pi   -   sqrt 3  / 4   * 36 = 3.261 cm2

May 10, 2021
#2
+862
0

Thank you!

AnimalMaster  May 10, 2021
#3
+498
+1

The area of a sector of a circle given the radius (r) and the angle (a) is $\frac{a}{360} \cdot r^2 \cdot \pi$

Here, the angle is $60$ and the radius is $6$ so we have $\frac{60}{360} \cdot 6^2 \pi= \frac{1}{6} \cdot 36 \pi = 6 \pi.$

The area of the equilateral triangle: We first must know the height and width, which is 6, but we do not know the height(I am assuming we do not know the formula for the area of an equilateral triangle.) Let the height be $h.$ We have $(\frac{6}{2})^2 + h^2 = 6^2 \Rightarrow 9 + h^2 = 36 \Rightarrow h^2 = 27 = 3 \sqrt{3}.$

The height is $3\sqrt{3},$ so the area is $\frac{1}{2} \cdot 3\sqrt{3} \cdot 6 = 9 \sqrt{3}.$

The answer is the sector - equilateral triangle = $6 \pi - 9 \sqrt{3}.$

May 10, 2021
user
The text passage contains a mathematical question about finding the area of a segment of a circle, and multiple answers are provided in the subsequent comments.

TYPE: SINGLE_QUESTION_WITH_ANSWER