Mixing
Cutting out a cylinder of maximum possibe size from a cube
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A cylinder of maximum possible size is cut out from a solid wooden cube. How much material is lost in the process?
What I could think is as follows:
Suppose the cube is of a side $a,$ so the volume is $a^3$.
However that cylinder cut out from it must be having a height of $a$ but what about the radius?
geometry discrete-mathematics
edited Jan 7 at 15:16
amWhy
1
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
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add a comment |
$begingroup$
A cylinder of maximum possible size is cut out from a solid wooden cube. How much material is lost in the process?
What I could think is as follows:
Suppose the cube is of a side $a,$ so the volume is $a^3$.
However that cylinder cut out from it must be having a height of $a$ but what about the radius?
geometry discrete-mathematics
edited Jan 7 at 15:16
amWhy
1
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
$endgroup$
$begingroup$
Why must the height be $a?$ Why couldn't the axis of the cylinder be a diagonal of the cube, for instance? Not saying it is, just that possibilities like this need to be considered.
$endgroup$
– saulspatz
Jan 7 at 15:07
2
$begingroup$
I mean, if you have already decided that the height should be $a$ (i.e. the axis of the cylinder is parallel to an edge of the cube), then the maximum radius would be $a/2$
$endgroup$
– glowstonetrees
Jan 7 at 15:23
add a comment |
$begingroup$
A cylinder of maximum possible size is cut out from a solid wooden cube. How much material is lost in the process?
What I could think is as follows:
Suppose the cube is of a side $a,$ so the volume is $a^3$.
However that cylinder cut out from it must be having a height of $a$ but what about the radius?
geometry discrete-mathematics
edited Jan 7 at 15:16
amWhy
1
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
$endgroup$
A cylinder of maximum possible size is cut out from a solid wooden cube. How much material is lost in the process?
What I could think is as follows:
Suppose the cube is of a side $a,$ so the volume is $a^3$.
However that cylinder cut out from it must be having a height of $a$ but what about the radius?
geometry discrete-mathematics
geometry discrete-mathematics
edited Jan 7 at 15:16
amWhy
1
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
edited Jan 7 at 15:16
amWhy
1
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
edited Jan 7 at 15:16
amWhy
1
edited Jan 7 at 15:16
amWhy
1
edited Jan 7 at 15:16
amWhy
1
1
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
asked Jan 7 at 15:04
satyajeet jhasatyajeet jha
162
162
$begingroup$
Why must the height be $a?$ Why couldn't the axis of the cylinder be a diagonal of the cube, for instance? Not saying it is, just that possibilities like this need to be considered.
$endgroup$
– saulspatz
Jan 7 at 15:07
2
$begingroup$
I mean, if you have already decided that the height should be $a$ (i.e. the axis of the cylinder is parallel to an edge of the cube), then the maximum radius would be $a/2$
$endgroup$
– glowstonetrees
Jan 7 at 15:23
add a comment |
$begingroup$
Why must the height be $a?$ Why couldn't the axis of the cylinder be a diagonal of the cube, for instance? Not saying it is, just that possibilities like this need to be considered.
$endgroup$
– saulspatz
Jan 7 at 15:07
2
$begingroup$
I mean, if you have already decided that the height should be $a$ (i.e. the axis of the cylinder is parallel to an edge of the cube), then the maximum radius would be $a/2$
$endgroup$
– glowstonetrees
Jan 7 at 15:23
$begingroup$
Why must the height be $a?$ Why couldn't the axis of the cylinder be a diagonal of the cube, for instance? Not saying it is, just that possibilities like this need to be considered.
$endgroup$
– saulspatz
Jan 7 at 15:07
$begingroup$
Why must the height be $a?$ Why couldn't the axis of the cylinder be a diagonal of the cube, for instance? Not saying it is, just that possibilities like this need to be considered.
$endgroup$
– saulspatz
Jan 7 at 15:07
2
2
$begingroup$
I mean, if you have already decided that the height should be $a$ (i.e. the axis of the cylinder is parallel to an edge of the cube), then the maximum radius would be $a/2$
$endgroup$
– glowstonetrees
Jan 7 at 15:23
$begingroup$
I mean, if you have already decided that the height should be $a$ (i.e. the axis of the cylinder is parallel to an edge of the cube), then the maximum radius would be $a/2$
$endgroup$
– glowstonetrees
Jan 7 at 15:23
add a comment |
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$begingroup$
Why must the height be $a?$ Why couldn't the axis of the cylinder be a diagonal of the cube, for instance? Not saying it is, just that possibilities like this need to be considered.
$endgroup$
– saulspatz
Jan 7 at 15:07
2
$begingroup$
I mean, if you have already decided that the height should be $a$ (i.e. the axis of the cylinder is parallel to an edge of the cube), then the maximum radius would be $a/2$
$endgroup$
– glowstonetrees
Jan 7 at 15:23