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
The real numbers $x$ and $y$ are such that \begin{align*} x + y &= 4, \\ x^2 + y^2 &= 22, \\ x^4 &= y^4 - 176 \sqrt{
tamaranim1 [39]

You get everything you need from factoring the last expression:

x^4-y^4=-176\sqrt7

The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with

x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)

Plug in everything you know and solve for x-y:

-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}

4 0
3 years ago
Read 2 more answers
Help me please I'm not good At math
Andrei [34K]
What exactly do you need help with

4 0
3 years ago
Sum of all digits in integers from one and a billion.
Daniel [21]

Answer:

The is coming this:-

500,000,500,000

Did you get this in vedantu

8 0
3 years ago
Which of the following graphs represent a nonproportional relationship? Select all that apply.
natka813 [3]

Answer:

2nd, 4th and 5th one

Step-by-step explanation:

Hey There!

So remember in order for it to be a proportional relationship it has to be a straight line and it has to go through the origin (0,0)

The 2nd, 4th and 5th ones are non proportional relationships

Why? Well because they don't go through the origin

3 0
3 years ago
Read 2 more answers
The Problem:
rosijanka [135]

Answer: ever find out???

3 0
3 years ago
Read 2 more answers
Other questions:
  • If angle 1 is 150°, what is angle 4 and angle 7?
    6·1 answer
  • HELP ME PLEASAAASE I WANNA PASS
    15·1 answer
  • Is the graph a function or not? Why or why not?
    14·2 answers
  • Which is a better estimate for the volume of a coffee mug?<br><br> A)15 pints <br> B)15 fluid ounces
    13·2 answers
  • A bike store sells scooters at a 54% markup. If the store bought each scooter for $29.25, what is the resale price to the neares
    13·2 answers
  • Angle efb is 80 what is the the size of angle x
    14·1 answer
  • (g + 12) ÷ h as a fraction plz i need help
    7·1 answer
  • Bill claims that he found the actual December temperature by adding either –5 + 3 or 3 + –5.
    5·1 answer
  • SOMEONE PLEASE HELP !
    14·2 answers
  • Find the area of the surface the part of the plane y=x^2 y^2 cylinder x^2 z^2=16
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!