Cube inscribed in a hemi-spherical shape
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What should be the approach to determine the distance? It seems that we need to form a Pythagorean triangle for this one. If it was a cube inside a sphere we could have easily said that the diameter of the sphere will be equal to the diagonal of the cube. But I am not able to visualize this problem.
geometry
edited Dec 27 '18 at 19:22
dantopa
6,68442245
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
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add a comment |
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What should be the approach to determine the distance? It seems that we need to form a Pythagorean triangle for this one. If it was a cube inside a sphere we could have easily said that the diameter of the sphere will be equal to the diagonal of the cube. But I am not able to visualize this problem.
geometry
edited Dec 27 '18 at 19:22
dantopa
6,68442245
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
$endgroup$
1
$begingroup$
Welcome the Mathematics Stack Exchange. A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here. For typesetting your equations, please use MathJax: math.meta.stackexchange.com/questions/5020/…
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– dantopa
Dec 27 '18 at 19:21
1
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Hint: Let $O$ be the common center of the base and the hemisphere and $C$ be the vertex of cube above $B$. What is the relationship between $|AB|$ and $|OC|$?
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– achille hui
Dec 27 '18 at 19:30
add a comment |
$begingroup$
What should be the approach to determine the distance? It seems that we need to form a Pythagorean triangle for this one. If it was a cube inside a sphere we could have easily said that the diameter of the sphere will be equal to the diagonal of the cube. But I am not able to visualize this problem.
geometry
edited Dec 27 '18 at 19:22
dantopa
6,68442245
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
$endgroup$
What should be the approach to determine the distance? It seems that we need to form a Pythagorean triangle for this one. If it was a cube inside a sphere we could have easily said that the diameter of the sphere will be equal to the diagonal of the cube. But I am not able to visualize this problem.
geometry
geometry
edited Dec 27 '18 at 19:22
dantopa
6,68442245
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
edited Dec 27 '18 at 19:22
dantopa
6,68442245
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
edited Dec 27 '18 at 19:22
dantopa
6,68442245
edited Dec 27 '18 at 19:22
dantopa
6,68442245
edited Dec 27 '18 at 19:22
dantopa
6,68442245
6,68442245
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
asked Dec 27 '18 at 19:15
Ritwik BhattacharyyaRitwik Bhattacharyya
1
1
1
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Welcome the Mathematics Stack Exchange. A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here. For typesetting your equations, please use MathJax: math.meta.stackexchange.com/questions/5020/…
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– dantopa
Dec 27 '18 at 19:21
1
$begingroup$
Hint: Let $O$ be the common center of the base and the hemisphere and $C$ be the vertex of cube above $B$. What is the relationship between $|AB|$ and $|OC|$?
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– achille hui
Dec 27 '18 at 19:30
add a comment |
1
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Welcome the Mathematics Stack Exchange. A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here. For typesetting your equations, please use MathJax: math.meta.stackexchange.com/questions/5020/…
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– dantopa
Dec 27 '18 at 19:21
1
$begingroup$
Hint: Let $O$ be the common center of the base and the hemisphere and $C$ be the vertex of cube above $B$. What is the relationship between $|AB|$ and $|OC|$?
$endgroup$
– achille hui
Dec 27 '18 at 19:30
1
1
$begingroup$
Welcome the Mathematics Stack Exchange. A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here. For typesetting your equations, please use MathJax: math.meta.stackexchange.com/questions/5020/…
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– dantopa
Dec 27 '18 at 19:21
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Welcome the Mathematics Stack Exchange. A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here. For typesetting your equations, please use MathJax: math.meta.stackexchange.com/questions/5020/…
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– dantopa
Dec 27 '18 at 19:21
1
1
$begingroup$
Hint: Let $O$ be the common center of the base and the hemisphere and $C$ be the vertex of cube above $B$. What is the relationship between $|AB|$ and $|OC|$?
$endgroup$
– achille hui
Dec 27 '18 at 19:30
$begingroup$
Hint: Let $O$ be the common center of the base and the hemisphere and $C$ be the vertex of cube above $B$. What is the relationship between $|AB|$ and $|OC|$?
$endgroup$
– achille hui
Dec 27 '18 at 19:30
add a comment |
2 Answers
2
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The distance from a corner at the base to the center of the top is the same as the distance from the center of the base to a corner at the top. This length is the radius of the hemisphere: $10$m
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
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add a comment |
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Let $O$ be a center of our sphere and $K$ be a top left vertex of the cuboid.
Now, easy to see that $OKAB$ is a parallelogram ($AK||OB$ and $AK=OB$), which gives $$AB=OK=frac{20}{2}=10.$$
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
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add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
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votes
$begingroup$
The distance from a corner at the base to the center of the top is the same as the distance from the center of the base to a corner at the top. This length is the radius of the hemisphere: $10$m
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
$endgroup$
add a comment |
$begingroup$
The distance from a corner at the base to the center of the top is the same as the distance from the center of the base to a corner at the top. This length is the radius of the hemisphere: $10$m
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
$endgroup$
add a comment |
$begingroup$
The distance from a corner at the base to the center of the top is the same as the distance from the center of the base to a corner at the top. This length is the radius of the hemisphere: $10$m
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
$endgroup$
The distance from a corner at the base to the center of the top is the same as the distance from the center of the base to a corner at the top. This length is the radius of the hemisphere: $10$m
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
answered Dec 27 '18 at 19:30
Daniel MathiasDaniel Mathias
1,40518
1,40518
add a comment |
add a comment |
$begingroup$
Let $O$ be a center of our sphere and $K$ be a top left vertex of the cuboid.
Now, easy to see that $OKAB$ is a parallelogram ($AK||OB$ and $AK=OB$), which gives $$AB=OK=frac{20}{2}=10.$$
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
$endgroup$
add a comment |
$begingroup$
Let $O$ be a center of our sphere and $K$ be a top left vertex of the cuboid.
Now, easy to see that $OKAB$ is a parallelogram ($AK||OB$ and $AK=OB$), which gives $$AB=OK=frac{20}{2}=10.$$
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
$endgroup$
add a comment |
$begingroup$
Let $O$ be a center of our sphere and $K$ be a top left vertex of the cuboid.
Now, easy to see that $OKAB$ is a parallelogram ($AK||OB$ and $AK=OB$), which gives $$AB=OK=frac{20}{2}=10.$$
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
$endgroup$
Let $O$ be a center of our sphere and $K$ be a top left vertex of the cuboid.
Now, easy to see that $OKAB$ is a parallelogram ($AK||OB$ and $AK=OB$), which gives $$AB=OK=frac{20}{2}=10.$$
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
answered Dec 30 '18 at 19:33
Michael RozenbergMichael Rozenberg
110k1896201
110k1896201
add a comment |
add a comment |
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Welcome the Mathematics Stack Exchange. A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here. For typesetting your equations, please use MathJax: math.meta.stackexchange.com/questions/5020/…
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– dantopa
Dec 27 '18 at 19:21
1
$begingroup$
Hint: Let $O$ be the common center of the base and the hemisphere and $C$ be the vertex of cube above $B$. What is the relationship between $|AB|$ and $|OC|$?
$endgroup$
– achille hui
Dec 27 '18 at 19:30