A community for students.
Here's the question you clicked on:
 0 viewing
terricherri
 3 years ago
Find the area of the shaded portion in the circle.
click pic below
terricherri
 3 years ago
Find the area of the shaded portion in the circle. click pic below

This Question is Closed

Curry
 3 years ago
Best ResponseYou've already chosen the best response.0i think 24 pi but not sure dont enter that its just a suggestion but its 18pi + something

robtobey
 3 years ago
Best ResponseYou've already chosen the best response.1Shaded area is the area of a half circle plus the area of the indicated segment.\[\frac{\pi r^2}{2}+\frac{1}{2}r{}^{\wedge}2(\theta \text{Sin}[\theta ])\text{ where } \theta =\pi 2\text{ArcSin}\left[\frac{6}{12}\right]\text{and } r=6 \]\[18 \left(\frac{\sqrt{3}}{2}+\frac{2 \pi }{3}\right)+18 \pi =78.6593 \]

Parsa
 3 years ago
Best ResponseYou've already chosen the best response.0The area of the shaded part is the are of the circle minus the area of the bright part; so it's better to find the area of the bright part instead. Connect the 3 lines as shown in the attached photo. You will have 2 equal triangles and 2 equal pieces of circle. The radius is 12/2 = 6. Using the arc functions, find the angle "a". Now You can easily find the area of the bright part and hence, also the shaded part. Area of the triangle is 3*6/2 = 9. Area of the small piece of circle is: \[\Pi(6^{2})\div \tan^{1} (3/6) =4.25\] Add them and multiply by two to find the total area of the bright part and we have: 26.51. So the area of the shaded part is: π(36) 26.51 = 86.53

robtobey
 3 years ago
Best ResponseYou've already chosen the best response.1@Parsa A detailed solution with comments using the Calculus and your approach is attached. You might recheck the dimensions on your triangle. The one dimensioned 6 on one of sides is actually 3*radical 3. The solution first posted by me as 78.6593 above is correct and comes from a general formula for a circle's segment area. Both of the attached solutions support 78.6593 as the numerical answer and the following symbolic answer:\[30 \pi 9 \sqrt{3} \]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.