Doubled: Volume increased 8 times
Tripled: Volume increased 27 times
Quadrupled: Volume increased 64 times
Pretty simple... if you're doubling the lengths, you're increasing them by 2 times. Take 2 and raise it to the 3rd power. If you're tripling the lengths, you're increasing them 3 times over. Take 3 and raise it to the 3rd power. And so on.
Doubled = 2^3 = 8
Tripled = 3^3 = 27
Quadrupled = 4^3 = 64
Does that make sense?
2007-01-29 16:49:59
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answer #1
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answered by Anonymous
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Helmut is getting very close to a lucid explanation.
All you have to do is set up a simple ratio to find a general formula for each case.
Let V be the original volume, and s be the original edge of the cube. Then V = s³.
Let V' be the volume when s is doubled and s' be 2s. Then V' = (s')³ = (2s)³ = 8s³.
We can then set up this ratio:
V' / V = 8s³ / s³
V' / V = 8 or
V' = 8 V
In other words, when the length of a side is doubled, the volume is multiplied 8 times.
If you triple s, then the resulting volume in terms of the new edge is (s')³ = (3s)³ = 27s³, giving us:
V' / V = 27 or
V' = 27 V.
When the length of the side is tripled, the volume is multiplied by a factor of 27.
If s is multiplied by 4, then V' = (s')³ = (4s)³ = 64s³. So we get:
V' / V = 64 or
V' = 64 V.
When the length of the edge of a cube is quadrupled, its volume is increased by a factor of 64.
This is about as simple as one can get when finding formulas to relate varying volumes with their corresponding base cubes.
2007-01-29 18:40:46
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answer #2
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answered by MathBioMajor 7
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V1 = s^3 where s is the length of one or any side
V2 = (2s)^3 = (2^3)(s^3) = 8s^3 so doubled means 8x more volume
V3 = (3^3)(s^3) = 27s^3 or 27x more the original volume
V4 = 64s^3 or 64x times more and so on..
So, do you see a pattern?
Thus, the General formula then is V = ( n^3 )(s^3) where n can take on value from 1, 2, 3 ....etc.
2007-01-29 16:52:02
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answer #3
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answered by Aldo 5
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Start simple.
Whether you talk in inches & cubic inches, metres and cubic metres, you still get- 1x1x1 = 1
This can be written as 1 "to the power of 3", or 1 cubed or 1^3
Double the sides, and you get 2x2x2 = 8
This is 2 cubed, or 2^3
Triple gives- 3x3x3 = 27 3 cubed, or 3^3
SO- take the multiple (double, triple, whatever) and cube it, ie. multiply it by itself 3 times. That will give you how much the volume has changed.
2007-01-29 16:53:00
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answer #4
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answered by Alan 6
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Well you simply think about it in terms of x.
Let x equal the edge length.
Volume is Length*Width*Height right?
and all cubes have Length=Width=Height right?
Well First I will use a cube of x length for an example.
x*x*x=x^3
it then follows if I double the edge length I would have 2x for the Length, Width, and Height.
So
2x*2x*2x=8x^3
and from that I can triple the edge and get.
3x*3x*3x=27x^3
Quadrupled is simply with four.
Try it :)
2007-01-29 16:51:06
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answer #5
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answered by NightWindZero 2
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Vol Of Cube
2016-10-30 21:04:39
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answer #6
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answered by Anonymous
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Let the original length of the cube is x
Therefore,its volume is x^3
When the edge length is 2x,vol. will be (2x)^3=8x^3
When it is trebled.vol is (3x)^3=27x^3
When it is quadrupled,it becomes(4x)^3=64x^3
So volume increases steadily to 2^3,3^3,4^3,5^3,6^3 times and so on
2007-01-29 16:55:13
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answer #7
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answered by alpha 7
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volume of a cube =a*a*a
when side is doubled
volume =2a*2a*2a
=8a^3
tripled
=3a*3a*3a
=27a^3
quadrupled
=4a*4a*4a
=64a^3
let x be many ever times the side of the cube is increased
volume would also increase as a cube of tht number
for doublw =2^3=8 etc
hence, the volume would always be equal to
=(x*a)^3
2007-01-29 16:54:59
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answer #8
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answered by phalo 1
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Take X to be original length, Vol = X^3
When X is doubled, VOL = (2X)^3
when it is tripled, VOL = (3X)^3.
2007-01-29 16:55:37
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answer #9
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answered by Jex 1
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Reiterating,
V = S^3
V2/V1 = S2^3/S1^3
If Sn = nS1,
Vn/V1 = n^3S1^3/S1^3
Vn/V1 = n^3
Vn = V1*n^3
V1 = V1
V2 = 8V1 (S2 = 2S1)
V3 = 27V1 (S3 = 3S1)
For surface area,
A = 6S^2
An/A1 = n^2
An = A1*n^2
2007-01-29 16:57:43
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answer #10
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answered by Helmut 7
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