1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Valentin [98]
1 year ago
14

In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree

measure of angle Q, the central angle of the shaded sect

Mathematics
1 answer:
Dmitriy789 [7]1 year ago
6 0
72^{\circ}

1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.

2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:

\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\  \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\  \\ 500\pi+\frac{125\piα}{72}=625\pi \\  \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi  \\  \\ \frac{125\pi α}{72}=125\pi  \\  \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi  \\  \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\  \\ α=72^{\circ} \\  \\  \end{gathered}

Thus, the centra angle of that shaded area is 72º

You might be interested in
A computer technician charges $60 to come to a home to repair a
-Dominant- [34]
5 hours
Hope this helps!
4 0
3 years ago
Read 2 more answers
432 students went on a field trip. Eight buses were filled with students. The
olga_2 [115]
Each bus was filled with 54 students
3 0
2 years ago
7m-17=60 solve one and two step equation
lord [1]

Answer:

11

Step-by-step explanation:

Hope it helps you :)

5 0
2 years ago
Read 2 more answers
The rule that best supports your answer to Question 5 would be:
mixas84 [53]
Sense the two triangles are congruent you would use CPCTC.
6 0
3 years ago
What is 2 3/2 equal to?<br><br> A. 2√8<br> B. 3√8<br> C. 3√16<br> D. 2√16
aivan3 [116]
2 3/2 is not equal to any of these
5 0
3 years ago
Other questions:
  • Kylie has $70 to spend on clothes. She wants to buy a pair of jeans for $30 and spend the rest on t-shirts. Each t-shirt costs $
    7·2 answers
  • Hiiii, can someone plz help me?
    14·1 answer
  • How long is the storage unit<br><br><br> This is Pythagorean theorem
    9·1 answer
  • 84 is 60% of what number?
    8·2 answers
  • Nine times a number is one more than ten times the number.
    11·1 answer
  • What angles are supplementary angles?
    7·2 answers
  • Please help me it’s very important please answer it correctly<br> Thank you
    14·1 answer
  • A4BC is a right-angled isosceles triangle and the area of AABC is 50 cm.
    8·1 answer
  • Kelly got a part time job and had to pay $150 worth of taxes, which was 10% of her monthly payment. How much money did she make
    11·2 answers
  • A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!