#1
I can't beleive i've been stuck on this one for a while:




the height is 2.5, the radius is 1.5


the formula for volume of cylinder is: ¶r2h (i got 17.67)


the volume of the hex prism is ????

so the final answer would be : Volume of Hex - volume of clylinder
#2
666
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#4
666
v CLICK v



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#7
Take the formula for volume of cylinder and divide it by zero to get the volume of a hex.
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#8
isn't there a formula for area for every polygon
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#9
Volume of any prism is

Volume = Area of the base * Height

Since the base of this one is in the shape of a regular polygon, we can use the equation

Area = 1/2 * Apothem * Perimeter

The apothem is a line from the center of the hexagon to the midpoint of one of the sides. So if we think of the hexagon as six equilateral triangles stuck together, the apothem is the altitude of one of the triangles. Also, you know the lengths of all sides of one of those triangles, so you can find the altitude (right?) and then you'd have the apothem. Then use the two equations and you have your answer.
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#10
Quote by aprescott_27
Volume of any prism is

Volume = Area of the base * Height

Since the base of this one is in the shape of a regular polygon, we can use the equation

Area = 1/2 * Apothem * Perimeter

The apothem is a line from the center of the hexagon to the midpoint of one of the sides. So if we think of the hexagon as six equilateral triangles stuck together, the apothem is the altitude of one of the triangles. Also, you know the lengths of all sides of one of those triangles, so you can find the altitude (right?) and then you'd have the apothem. Then use the two equations and you have your answer.



so is the apothem 3?, if not how would i calculate it?
#11
Give me a second, I need to make pictures (I'm horrible at explaining things with words.) I'll edit this post in a few.

EDIT:



So the green lines mark the boundaries of the equilateral triangles. The red line is the apothem of the hexagon (which also happens to be an altitude of one of the triangles.) To find the altitude of the triangle (and the apothem) we note that one half the equilateral triangle is a 30-60-90 triangle, which means that the length of the hypotenuse is twice the length of the short side, and the length of the long side is sqrt(3) (square root of three) times the short side. Which means in this case, the length of the altitude (and apothem) is 3 * sqrt(3) / 2. (That make any sense to you?)
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Last edited by aprescott_27 at Apr 28, 2008,
#13
Quote by Camaro_IRocz
so is the apothem 3?, if not how would i calculate it?



a^2+b^2 = c^2


Since you're finding the line from the vertex to the midpoint, cut the base in half, so 1.5 squared + b squared = 9


9 - 2.25 = 6.75

the apothem is 6.75 (I think. My geometry is incredibly rusty.)
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#15
Quote by HaKattack
a^2+b^2 = c^2


Since you're finding the line from the vertex to the midpoint, cut the base in half, so 1.5 squared + b squared = 9


9 - 2.25 = 6.75

the apothem is 6.75 (I think. My geometry is incredibly rusty.)



um if the apothem is 6.75, then the formula for volume of hex is:

1/2 x 6.75 x 18 x 2.5 = 151.875

so thats way too big because 151 minus 17.67 (volume of cylinder) is no were near the answer ranges

ill keep trying....
#16
Quote by MTVget0FFtheAIR
i got 40.7

thats close to answer D, did you really get that, or did u just make that up, becuase i remember my friend telling me that it was d, but i wanted to make sure
#17
Your cylinder is jacked up. The volume is 9pi*2.5

The volume of your cylinder is 70.65 when pi is 3.14.

EDIT: NVM, radius is 1.5, not 3.


Are you sure you have these numbers all right? I can't make any sense of this with those answers/measurements.
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Last edited by HaKattack at Apr 28, 2008,
#18
the apothem is 1.5root3. In a hexagon there are 6 equilateral triangles...all with a side of three. Draw an altitude from the top; because it's an isosceles triangle it divides the bottom into two congruent segments. The two right triangles you just created are both 30-60-90 triangles because one side is half of the hypoteneuse, which means that the height of the triangle has to be 1/2 hypoteneuse root 3.
right?
#19
ya the numbers are correct:

the diameter is 3

the length of one side of the hex is 3

the height is 2.5

Answers:

a 34.75
b 36
c 38.58
d. 40.79
e 42.22
#20
I was way off. The apothem is 1.5 times the square root of 3, which is 2.6.


2.6 * 2.5 (height) times 9 (half the perimeter) is 58.5, - 17.7 = 40.8? How close is that?

EDIT: You wrote answer D wrong in the original post -_-. It's 'D'. You're welcome.
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#21
The answer is 42.
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#22
See the edit to my post above.

The area of the base is 27 * sqrt(3) / 2, so the volume of the prism is 135 * sqrt(3) / 4 (approx. 58.46)

If the radius of the cylinder is 1.5, then the volume of the cylinder is 2.25 * 2.5 * pi (approx 17.67)

When you subtract the volume of the cylinder from the volume of the prism, you get 40.79.
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#23
Quote by aprescott_27
See the edit to my post above.

The area of the base is 27 * sqrt(3) / 2, so the volume of the prism is 135 * sqrt(3) / 4 (approx. 58.46)

If the radius of the cylinder is 1.5, then the volume of the cylinder is 2.25 * 2.5 * pi (approx 17.67)

When you subtract the volume of the cylinder from the volume of the prism, you get 40.79.



yaaaaaaaay for me and aprescott! Woohoo!

I used a different formula for the volume of the hex. prism (3ash), but it worked!
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#24
Quote by aprescott_27
See the edit to my post above.

The area of the base is 27 * sqrt(3) / 2, so the volume of the prism is 135 * sqrt(3) / 4 (approx. 58.46)

If the radius of the cylinder is 1.5, then the volume of the cylinder is 2.25 * 2.5 * pi (approx 17.67)

When you subtract the volume of the cylinder from the volume of the prism, you get 40.79.

Thanks a lot man and everyone who helped. ty ty ty ty ty ty
#25
Quote by Camaro_IRocz
thats close to answer D, did you really get that, or did u just make that up, becuase i remember my friend telling me that it was d, but i wanted to make sure

i really got it.

[(.5 x 3 x 1.5rad3) x 6 x 2.5] - (pi x 1.5squared x 2.5) = 40.7
[.5 x base x *height* x 6triangles x depth] - (pi x radius squared x depth)

*height* is found by 30-60-90 triangle rule.

i doubt this explanation will make sense....wait for darkstar?


edit: ooooh it's done. alright pit!


My mind is going. I can feel it.
#26
Quote by aprescott_27
Volume of any prism is

Volume = Area of the base * Height

Since the base of this one is in the shape of a regular polygon, we can use the equation

Area = 1/2 * Apothem * Perimeter

The apothem is a line from the center of the hexagon to the midpoint of one of the sides. So if we think of the hexagon as six equilateral triangles stuck together, the apothem is the altitude of one of the triangles. Also, you know the lengths of all sides of one of those triangles, so you can find the altitude (right?) and then you'd have the apothem. Then use the two equations and you have your answer.

Dude's got it. Very simple problem.