The figure shows that the polygon:
- Has 6 sides.
- Divided into 4 triangles.
- Total interior angle measure of 180°.
- Total measure of the interior angles of this polygon is 720°.
<h3>What is the polygon about?</h3>
The polygon has sides of: AB, BC, CD, DE, EF, FA.
So, this means that they have 6 sides and when you look at the diagram, this 6 sides can be divided into 4 triangle of which whose total interior will sum up to 180°.
Since there are 4 triangles and the interior is 180°, then to get the total measure of the interior angles of this polygon will be:
= 180 X 4 = 720
Therefore, one can say that the The figure shows that the polygon, has 6 sides, may be divided into 4 triangles, each of which will have a total interior angle measure of 180. Therefore, the total measure of the interior angles of this polygon is 720.
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Answer: 14/15
This is because to get to 14/15 you must divide by 6 but when getting to 42/45 you must divide 2. Therefore 14/15 is your answer because the problem went to the most reduced fraction.
Check the picture below.
since the diameter of the cone is 6", then its radius is half that or 3", so getting the volume of only the cone, not the top.
1)
![\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \implies V\approx 37.7](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20cone%7D%5C%5C%5C%5C%20V%3D%5Ccfrac%7B%5Cpi%20r%5E2%20h%7D%7B3%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D3%5C%5C%20h%3D4%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B%5Cpi%20%283%29%5E2%284%29%7D%7B3%7D%5Cimplies%20V%3D12%5Cpi%20%5Cimplies%20V%5Capprox%2037.7)
2)
now, the top of it, as you notice in the picture, is a semicircle, whose radius is the same as the cone's, 3.
![\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20sphere%7D%5C%5C%5C%5C%20V%3D%5Ccfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D3%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B4%5Cpi%20%283%29%5E3%7D%7B3%7D%5Cimplies%20V%3D36%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bhalf%20of%20that%20for%20a%20semisphere%7D%7D%7BV%3D18%5Cpi%20%7D%5Cimplies%20V%5Capprox%2056.55)
3)
well, you'll be serving the cone and top combined, 12π + 18π = 30π or about 94.25 in³.
4)
pretty much the same thing, we get the volume of the cone and its top, add them up.
11 by 16
Explanation:
Set up two equations
2
x
+
2
y
=
54
x
×
y
=
176
Solving the first equation for x
2
x
+
2
y
−
2
y
=
54
−
2
y
this gives
2
x
=
54
−
2
y
Divide both sides by 2
(
2
x
2
)
=
54
−
2
y
2
This gives.
x
=
27
−
y
putting this value into the second equation gives.
(
27
−
y
)
×
y
=
176
multiplying across the parenthesis gives
27
y
−
y
2
=
176
subtracting 176 from both sides gives
is
27
y
−
y
2
−
176
=
0
multiplying by negative one gives
−
27
y
+
y
2
+
176
=
0
factoring this into y gives
(
y
−
11
)
×
(
y
−
16
)
=
0
Solving for both y's gives
y
=
11
,
y
=
16
