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
Ede4ka [16]
3 years ago
15

The figure shown below is composed of a semicircle and a non-overlapping equilateral triangle and contains a hole that is also c

omposed of a semicircle and a non-overlapping equilateral triangle. if the radius of the larger semicircle is 8, and the radius of the smaller semicircle is ⅓, find the area of the figure.

Mathematics
1 answer:
Sloan [31]3 years ago
3 0

Check the picture below.

since we know the radius of the larger semicircle is 8, thus its diameter is 16, which is the length of one side of the equilateral triangle.  We also know the smaller semicircle has a radius of 1/3, and thus a diameter of 2/3, namely the lenght of one side of the small equilateral triangle.

now, if we just can get the area of the larger figure and the area of the smaller one and subtract the smaller from the larger, we'll be in effect making a hole/gap in the larger and what's leftover is the shaded figure.

\bf \stackrel{\textit{area of a semi-circle}}{A=\cfrac{1}{2}\pi r^2\qquad r=radius}~\hspace{10em}\stackrel{\textit{area of an equilateral triangle}}{A=\cfrac{s^2\sqrt{3}}{4}\qquad s=\stackrel{side's}{length}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\left[ \stackrel{\textit{larger figure}}{\cfrac{1}{2}\pi 8^2~~+~~\cfrac{16^2\sqrt{3}}{4}} \right]\qquad -\qquad \left[ \cfrac{1}{2}\pi \left( \cfrac{1}{3} \right)^2 +\cfrac{\left( \frac{2}{3} \right)^2\sqrt{3}}{4}\right]}

\bf \left[ 32\pi +64\sqrt{3} \right]\qquad -\qquad \left[ \cfrac{\pi }{18}+\cfrac{\frac{4}{9}\sqrt{3}}{4} \right] \\\\\\ \left[ 32\pi +64\sqrt{3} \right]\qquad -\qquad \left[ \cfrac{\pi }{18}+\cfrac{\sqrt{3}}{9} \right]~~\approx~~ 211.38 - 0.37~~\approx~~ 211.01

You might be interested in
1. In this Vacation time, go through your neigh blurs and take a survey (not less than 20 peoples) about their favourite festiva
JulsSmile [24]

Answer:

1

Step-by-step explanation:

dgshdbahdbdbsbdbdbdbdbebdbdhdhd

6 0
2 years ago
3( x + 4y + 6) - 2(x + 8y + 3).​
ser-zykov [4K]

Answer:

x-4y+12

Step-by-step explanation:

4 0
2 years ago
What is 8690 rounded off to the neareset hundred?<br>am just asking​
Lelu [443]

Answer:

8700

Step-by-step explanation:

If it is 8,690 and you round to the nearest hundred it would add one to 90 making it 8,700

3 0
3 years ago
Read 2 more answers
Please help me! Reward will be brainliest!
puteri [66]

Answer:

(9, 12)

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Which expression shows how to multiply 5x381 by using place value and exxpanded form?
Dovator [93]
<span><span>1.       </span>We have the given number = 5 x 381
Let’s show how to multiply this given equation using its expanded form and place value
=> 5 x 381
since we’re multiplying, we will start with the ones value which is 1
=> 5 x 1 = 5
Second is on the tens value
=> 5 x 80 = 400
Third is the hundreds value
=> 5 x 300 = 1 500
Now, we already have the answer to each values. Add
=> 1 500 + 400 + 5
=> 1 905</span>



5 0
2 years ago
Other questions:
  • How to solve 7(1+4n)+4
    15·1 answer
  • The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1
    9·1 answer
  • An ice chest contains 3 types of drinks: 10 apple juries 15 grape juices and 15 bottles of water what is the probability of gett
    13·1 answer
  • What is -282 -20,320 written out
    11·2 answers
  • In the regular octagon, the numeric value of the area of the shaded region is twice more than the numeric value of the length of
    7·1 answer
  • Explain the steps you would take to complete this conversion problem.
    11·1 answer
  • Solve the math problem
    12·1 answer
  • What are 43.6÷8 use compatible numbers using the quotient
    7·1 answer
  • Given that
    11·1 answer
  • Which fraction is equivalent to StartFraction 2 Over 6 EndFraction? StartFraction 3 Over 7 EndFraction, because StartFraction 2
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!