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How can I get precisely a certain cubic cm by changing the following factors?
Validity of proof for surface area of a sphereAngle and circle intersection, find the circular segment areaCuboid: Given Volume, Surface Area, length of one side / Find remaining sidesDecomposition if matrix with strongly correlated columnsTwo approaches to the Volume of a Drilled Sphere (Self-Answered, open to other answers)Certain chords of a parameterized parabola pass through a common pointPigeonhole principle in geometric taskSolid Mensuration ProblemCalculus Parcel Optimisation ProblemHow to calculate volume of an intersection between a hyperrectangle and an N-dimensional ball in multiple dimensions
$begingroup$
By a calculation of the size of the cubic cm which its sizes are: 3.8330 * 3.8330 * 5.17455, I got a volume of 76.02. How can I get precisely '''76.04''' cubic cm, by changing the first two mentioned factors (i.e. 3.8330 * 3.8330 * 5.17455) equally?
N.b. I tried many ways and I couldn't find it, always I got more or less but not precisely.
geometry
New contributor
$endgroup$
add a comment |
$begingroup$
By a calculation of the size of the cubic cm which its sizes are: 3.8330 * 3.8330 * 5.17455, I got a volume of 76.02. How can I get precisely '''76.04''' cubic cm, by changing the first two mentioned factors (i.e. 3.8330 * 3.8330 * 5.17455) equally?
N.b. I tried many ways and I couldn't find it, always I got more or less but not precisely.
geometry
New contributor
$endgroup$
add a comment |
$begingroup$
By a calculation of the size of the cubic cm which its sizes are: 3.8330 * 3.8330 * 5.17455, I got a volume of 76.02. How can I get precisely '''76.04''' cubic cm, by changing the first two mentioned factors (i.e. 3.8330 * 3.8330 * 5.17455) equally?
N.b. I tried many ways and I couldn't find it, always I got more or less but not precisely.
geometry
New contributor
$endgroup$
By a calculation of the size of the cubic cm which its sizes are: 3.8330 * 3.8330 * 5.17455, I got a volume of 76.02. How can I get precisely '''76.04''' cubic cm, by changing the first two mentioned factors (i.e. 3.8330 * 3.8330 * 5.17455) equally?
N.b. I tried many ways and I couldn't find it, always I got more or less but not precisely.
geometry
geometry
New contributor
New contributor
edited 1 hour ago
Ubiquitous Student
New contributor
asked 3 hours ago
Ubiquitous StudentUbiquitous Student
1114
1114
New contributor
New contributor
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
You have $3.833 times 3.833 times5.174=76.02 .$
You can change it by multiplying both sides by $displaystyle frac76.0476.02$.
We then have $3.833 times 3.833 times5.174 times displaystyle frac76.0476.02=76.02 times displaystyle frac76.0476.02$.
This comes out to $3.833 times 3.833 times5.17564=76.04 $
$endgroup$
1
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
|
show 1 more comment
$begingroup$
Actually $3.833 cdot 3.833 cdot 5.174 = 76.0158$ so the added volume will be $.0242$
One way is to think of it as adding a sheet $3.833 cdot 3.833$ with a volume of $0.0242 textcm^3$. How thick does it have to be to equal that volume?
Hence, $frac0.02423.833^2 = .00165$
So the dimensions will be $3.833 cdot 3.833 cdot (5.174 + .00165)$
$3.833 cdot 3.833 cdot 5.17565 = 76.040$
$endgroup$
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
add a comment |
$begingroup$
To avoid getting caught-up in specific numbers ...
Suppose you have
$$acdot b cdot c = d$$
but you want $d$ to become $e$. You can make this happen by multiplying both sides by $e/d$:
$$left(acdot b cdot c right)cdot fraced = dcdotfraced = e$$
Now, you can use the left-hand side's factor of $e/d$ to make adjustments to $a$, $b$, and/or $c$. If you just wanted to adjust one factor, you could write, say,
$$left( acdot fracedright)cdot bcdot c ;=; e tag1$$
If you wanted to adjust two factors proportionally (as is specifically requested in the question), you can "split" $e/d$ equally across the factors using a square root:
$$fraced = sqrtfracedcdotsqrtfraced qquadtoqquadleft(acdot sqrtfracedright)cdotleft(bcdot sqrtfracedright)cdot c ;=; e tag2$$
Finally, if you later decide you actually want to adjust your entire box proportionally, you can use cube roots:
$$left(acdotsqrt[3]fracedright)cdotleft(bcdotsqrt[3]fracedright)cdot left(ccdotsqrt[3]fracedright) ;=; e tag3$$
Naturally, the same type of thing works with any number of overall factors and desired adjustments, using higher-level roots as needed.
$endgroup$
add a comment |
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3 Answers
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active
oldest
votes
3 Answers
3
active
oldest
votes
active
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active
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$begingroup$
You have $3.833 times 3.833 times5.174=76.02 .$
You can change it by multiplying both sides by $displaystyle frac76.0476.02$.
We then have $3.833 times 3.833 times5.174 times displaystyle frac76.0476.02=76.02 times displaystyle frac76.0476.02$.
This comes out to $3.833 times 3.833 times5.17564=76.04 $
$endgroup$
1
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
|
show 1 more comment
$begingroup$
You have $3.833 times 3.833 times5.174=76.02 .$
You can change it by multiplying both sides by $displaystyle frac76.0476.02$.
We then have $3.833 times 3.833 times5.174 times displaystyle frac76.0476.02=76.02 times displaystyle frac76.0476.02$.
This comes out to $3.833 times 3.833 times5.17564=76.04 $
$endgroup$
1
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
|
show 1 more comment
$begingroup$
You have $3.833 times 3.833 times5.174=76.02 .$
You can change it by multiplying both sides by $displaystyle frac76.0476.02$.
We then have $3.833 times 3.833 times5.174 times displaystyle frac76.0476.02=76.02 times displaystyle frac76.0476.02$.
This comes out to $3.833 times 3.833 times5.17564=76.04 $
$endgroup$
You have $3.833 times 3.833 times5.174=76.02 .$
You can change it by multiplying both sides by $displaystyle frac76.0476.02$.
We then have $3.833 times 3.833 times5.174 times displaystyle frac76.0476.02=76.02 times displaystyle frac76.0476.02$.
This comes out to $3.833 times 3.833 times5.17564=76.04 $
answered 3 hours ago
Saketh MalyalaSaketh Malyala
7,7041535
7,7041535
1
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
|
show 1 more comment
1
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
1
1
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
+1 Note that you can multiply any one of the three factors by $76.04/75.02$, although there's an aesthetic argument for keeping the first two equal.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
@UbiquitousStudent do you want to change both of the first two parameters? or just one of them?
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
you can multiply 3.833 by 76.04/76.02 instead
$endgroup$
– Saketh Malyala
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
$begingroup$
You can take any two positive numbers $a$ and $b$, let $c = (76.04/76.02)/ab$ and then multiply each of the factors by $a$, $b$ and $c$. So you can make any two factors anything you like and adjust the third accordingly. If you want to keep the third factor the same and keep the first two equal, let $a = b =$ the square root of $76.04/76.02$.
$endgroup$
– Ethan Bolker
2 hours ago
|
show 1 more comment
$begingroup$
Actually $3.833 cdot 3.833 cdot 5.174 = 76.0158$ so the added volume will be $.0242$
One way is to think of it as adding a sheet $3.833 cdot 3.833$ with a volume of $0.0242 textcm^3$. How thick does it have to be to equal that volume?
Hence, $frac0.02423.833^2 = .00165$
So the dimensions will be $3.833 cdot 3.833 cdot (5.174 + .00165)$
$3.833 cdot 3.833 cdot 5.17565 = 76.040$
$endgroup$
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
add a comment |
$begingroup$
Actually $3.833 cdot 3.833 cdot 5.174 = 76.0158$ so the added volume will be $.0242$
One way is to think of it as adding a sheet $3.833 cdot 3.833$ with a volume of $0.0242 textcm^3$. How thick does it have to be to equal that volume?
Hence, $frac0.02423.833^2 = .00165$
So the dimensions will be $3.833 cdot 3.833 cdot (5.174 + .00165)$
$3.833 cdot 3.833 cdot 5.17565 = 76.040$
$endgroup$
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
add a comment |
$begingroup$
Actually $3.833 cdot 3.833 cdot 5.174 = 76.0158$ so the added volume will be $.0242$
One way is to think of it as adding a sheet $3.833 cdot 3.833$ with a volume of $0.0242 textcm^3$. How thick does it have to be to equal that volume?
Hence, $frac0.02423.833^2 = .00165$
So the dimensions will be $3.833 cdot 3.833 cdot (5.174 + .00165)$
$3.833 cdot 3.833 cdot 5.17565 = 76.040$
$endgroup$
Actually $3.833 cdot 3.833 cdot 5.174 = 76.0158$ so the added volume will be $.0242$
One way is to think of it as adding a sheet $3.833 cdot 3.833$ with a volume of $0.0242 textcm^3$. How thick does it have to be to equal that volume?
Hence, $frac0.02423.833^2 = .00165$
So the dimensions will be $3.833 cdot 3.833 cdot (5.174 + .00165)$
$3.833 cdot 3.833 cdot 5.17565 = 76.040$
answered 2 hours ago
Phil HPhil H
4,3752412
4,3752412
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
add a comment |
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
$begingroup$
Thank you very much for you answer (1+^). Is there a way to add change the first two parameters (3.833*3.833)? I mean even-though it'll be the same size, but if I want to change these dimensions is important.
$endgroup$
– Ubiquitous Student
2 hours ago
add a comment |
$begingroup$
To avoid getting caught-up in specific numbers ...
Suppose you have
$$acdot b cdot c = d$$
but you want $d$ to become $e$. You can make this happen by multiplying both sides by $e/d$:
$$left(acdot b cdot c right)cdot fraced = dcdotfraced = e$$
Now, you can use the left-hand side's factor of $e/d$ to make adjustments to $a$, $b$, and/or $c$. If you just wanted to adjust one factor, you could write, say,
$$left( acdot fracedright)cdot bcdot c ;=; e tag1$$
If you wanted to adjust two factors proportionally (as is specifically requested in the question), you can "split" $e/d$ equally across the factors using a square root:
$$fraced = sqrtfracedcdotsqrtfraced qquadtoqquadleft(acdot sqrtfracedright)cdotleft(bcdot sqrtfracedright)cdot c ;=; e tag2$$
Finally, if you later decide you actually want to adjust your entire box proportionally, you can use cube roots:
$$left(acdotsqrt[3]fracedright)cdotleft(bcdotsqrt[3]fracedright)cdot left(ccdotsqrt[3]fracedright) ;=; e tag3$$
Naturally, the same type of thing works with any number of overall factors and desired adjustments, using higher-level roots as needed.
$endgroup$
add a comment |
$begingroup$
To avoid getting caught-up in specific numbers ...
Suppose you have
$$acdot b cdot c = d$$
but you want $d$ to become $e$. You can make this happen by multiplying both sides by $e/d$:
$$left(acdot b cdot c right)cdot fraced = dcdotfraced = e$$
Now, you can use the left-hand side's factor of $e/d$ to make adjustments to $a$, $b$, and/or $c$. If you just wanted to adjust one factor, you could write, say,
$$left( acdot fracedright)cdot bcdot c ;=; e tag1$$
If you wanted to adjust two factors proportionally (as is specifically requested in the question), you can "split" $e/d$ equally across the factors using a square root:
$$fraced = sqrtfracedcdotsqrtfraced qquadtoqquadleft(acdot sqrtfracedright)cdotleft(bcdot sqrtfracedright)cdot c ;=; e tag2$$
Finally, if you later decide you actually want to adjust your entire box proportionally, you can use cube roots:
$$left(acdotsqrt[3]fracedright)cdotleft(bcdotsqrt[3]fracedright)cdot left(ccdotsqrt[3]fracedright) ;=; e tag3$$
Naturally, the same type of thing works with any number of overall factors and desired adjustments, using higher-level roots as needed.
$endgroup$
add a comment |
$begingroup$
To avoid getting caught-up in specific numbers ...
Suppose you have
$$acdot b cdot c = d$$
but you want $d$ to become $e$. You can make this happen by multiplying both sides by $e/d$:
$$left(acdot b cdot c right)cdot fraced = dcdotfraced = e$$
Now, you can use the left-hand side's factor of $e/d$ to make adjustments to $a$, $b$, and/or $c$. If you just wanted to adjust one factor, you could write, say,
$$left( acdot fracedright)cdot bcdot c ;=; e tag1$$
If you wanted to adjust two factors proportionally (as is specifically requested in the question), you can "split" $e/d$ equally across the factors using a square root:
$$fraced = sqrtfracedcdotsqrtfraced qquadtoqquadleft(acdot sqrtfracedright)cdotleft(bcdot sqrtfracedright)cdot c ;=; e tag2$$
Finally, if you later decide you actually want to adjust your entire box proportionally, you can use cube roots:
$$left(acdotsqrt[3]fracedright)cdotleft(bcdotsqrt[3]fracedright)cdot left(ccdotsqrt[3]fracedright) ;=; e tag3$$
Naturally, the same type of thing works with any number of overall factors and desired adjustments, using higher-level roots as needed.
$endgroup$
To avoid getting caught-up in specific numbers ...
Suppose you have
$$acdot b cdot c = d$$
but you want $d$ to become $e$. You can make this happen by multiplying both sides by $e/d$:
$$left(acdot b cdot c right)cdot fraced = dcdotfraced = e$$
Now, you can use the left-hand side's factor of $e/d$ to make adjustments to $a$, $b$, and/or $c$. If you just wanted to adjust one factor, you could write, say,
$$left( acdot fracedright)cdot bcdot c ;=; e tag1$$
If you wanted to adjust two factors proportionally (as is specifically requested in the question), you can "split" $e/d$ equally across the factors using a square root:
$$fraced = sqrtfracedcdotsqrtfraced qquadtoqquadleft(acdot sqrtfracedright)cdotleft(bcdot sqrtfracedright)cdot c ;=; e tag2$$
Finally, if you later decide you actually want to adjust your entire box proportionally, you can use cube roots:
$$left(acdotsqrt[3]fracedright)cdotleft(bcdotsqrt[3]fracedright)cdot left(ccdotsqrt[3]fracedright) ;=; e tag3$$
Naturally, the same type of thing works with any number of overall factors and desired adjustments, using higher-level roots as needed.
answered 1 hour ago
BlueBlue
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49.8k970158
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