Volume of a rectangular prism when the prism has walls [closed]

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An esky has a height of 50cm, a width of 25cm and a length of 75cm. The walls of the esky are 4cm thick on each side (including the lid). If it is filled with cold water, how many litres will it hold?



The answer is apparently 236cm², and apparently you have to subtract 8 from the height, length and width. I don't really understand why.




geometry volume




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closed as off-topic by Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz Aug 1 at 17:53


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Try to visualize the column of water that would be contained. Its dimensions can be deducted from the given information. If it's a rectangle, it's easy to calculate its volume once you have the dimensions.
    – Matti P.
    Aug 1 at 11:12










  • When I "subtract $8$ from the height, length and width" I get $(50-8)(25-8)(75-8) = 47838,$ and converting to liters gives $47.838$ liters. No idea where the $236$ came from. If you still don't understand, I suggest you edit the question to show the complete working (as far as you know it or can guess it) and anything else that you know about the problem.
    – David K
    Aug 1 at 11:15










  • You will probably need to show some formulas or equations; use MathJax to make these readable to other people. See math.stackexchange.com/help/notation
    – David K
    Aug 1 at 11:16














up vote
0
down vote

favorite












An esky has a height of 50cm, a width of 25cm and a length of 75cm. The walls of the esky are 4cm thick on each side (including the lid). If it is filled with cold water, how many litres will it hold?



The answer is apparently 236cm², and apparently you have to subtract 8 from the height, length and width. I don't really understand why.




geometry volume




share|cite|improve this question













closed as off-topic by Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz Aug 1 at 17:53


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Try to visualize the column of water that would be contained. Its dimensions can be deducted from the given information. If it's a rectangle, it's easy to calculate its volume once you have the dimensions.
    – Matti P.
    Aug 1 at 11:12










  • When I "subtract $8$ from the height, length and width" I get $(50-8)(25-8)(75-8) = 47838,$ and converting to liters gives $47.838$ liters. No idea where the $236$ came from. If you still don't understand, I suggest you edit the question to show the complete working (as far as you know it or can guess it) and anything else that you know about the problem.
    – David K
    Aug 1 at 11:15










  • You will probably need to show some formulas or equations; use MathJax to make these readable to other people. See math.stackexchange.com/help/notation
    – David K
    Aug 1 at 11:16












up vote
0
down vote

favorite









up vote
0
down vote

favorite











An esky has a height of 50cm, a width of 25cm and a length of 75cm. The walls of the esky are 4cm thick on each side (including the lid). If it is filled with cold water, how many litres will it hold?



The answer is apparently 236cm², and apparently you have to subtract 8 from the height, length and width. I don't really understand why.




geometry volume




share|cite|improve this question













An esky has a height of 50cm, a width of 25cm and a length of 75cm. The walls of the esky are 4cm thick on each side (including the lid). If it is filled with cold water, how many litres will it hold?



The answer is apparently 236cm², and apparently you have to subtract 8 from the height, length and width. I don't really understand why.





geometry volume





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 1 at 12:24









steenbergh

25017




25017









asked Aug 1 at 10:53









Gabriel Chee

32




32




closed as off-topic by Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz Aug 1 at 17:53


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz Aug 1 at 17:53


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Aretino, Claude Leibovici, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Try to visualize the column of water that would be contained. Its dimensions can be deducted from the given information. If it's a rectangle, it's easy to calculate its volume once you have the dimensions.
    – Matti P.
    Aug 1 at 11:12










  • When I "subtract $8$ from the height, length and width" I get $(50-8)(25-8)(75-8) = 47838,$ and converting to liters gives $47.838$ liters. No idea where the $236$ came from. If you still don't understand, I suggest you edit the question to show the complete working (as far as you know it or can guess it) and anything else that you know about the problem.
    – David K
    Aug 1 at 11:15










  • You will probably need to show some formulas or equations; use MathJax to make these readable to other people. See math.stackexchange.com/help/notation
    – David K
    Aug 1 at 11:16
















  • Try to visualize the column of water that would be contained. Its dimensions can be deducted from the given information. If it's a rectangle, it's easy to calculate its volume once you have the dimensions.
    – Matti P.
    Aug 1 at 11:12










  • When I "subtract $8$ from the height, length and width" I get $(50-8)(25-8)(75-8) = 47838,$ and converting to liters gives $47.838$ liters. No idea where the $236$ came from. If you still don't understand, I suggest you edit the question to show the complete working (as far as you know it or can guess it) and anything else that you know about the problem.
    – David K
    Aug 1 at 11:15










  • You will probably need to show some formulas or equations; use MathJax to make these readable to other people. See math.stackexchange.com/help/notation
    – David K
    Aug 1 at 11:16















Try to visualize the column of water that would be contained. Its dimensions can be deducted from the given information. If it's a rectangle, it's easy to calculate its volume once you have the dimensions.
– Matti P.
Aug 1 at 11:12




Try to visualize the column of water that would be contained. Its dimensions can be deducted from the given information. If it's a rectangle, it's easy to calculate its volume once you have the dimensions.
– Matti P.
Aug 1 at 11:12












When I "subtract $8$ from the height, length and width" I get $(50-8)(25-8)(75-8) = 47838,$ and converting to liters gives $47.838$ liters. No idea where the $236$ came from. If you still don't understand, I suggest you edit the question to show the complete working (as far as you know it or can guess it) and anything else that you know about the problem.
– David K
Aug 1 at 11:15




When I "subtract $8$ from the height, length and width" I get $(50-8)(25-8)(75-8) = 47838,$ and converting to liters gives $47.838$ liters. No idea where the $236$ came from. If you still don't understand, I suggest you edit the question to show the complete working (as far as you know it or can guess it) and anything else that you know about the problem.
– David K
Aug 1 at 11:15












You will probably need to show some formulas or equations; use MathJax to make these readable to other people. See math.stackexchange.com/help/notation
– David K
Aug 1 at 11:16




You will probably need to show some formulas or equations; use MathJax to make these readable to other people. See math.stackexchange.com/help/notation
– David K
Aug 1 at 11:16










1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










To show why we drop 8 cm on each dimension, let's sketch out one side of the esky*:



enter image description here



(* Not entirely to scale...)



The surface area of this side is 75x50 $cm^2$. The blue area is (75 - 4 - 4) x (50 - 4 - 4) = 67 x 42 $cm^2$. Don't mind the orange areas, you're not subtracting them twice. You can see that a little more clearly when we cheat a bit and move the blue area:



enter image description here



This is done on a 2D-plane to show the principle, but it holds for 3D volumes as well.






share|cite|improve this answer























  • THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
    – Gabriel Chee
    Aug 1 at 11:52

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










To show why we drop 8 cm on each dimension, let's sketch out one side of the esky*:



enter image description here



(* Not entirely to scale...)



The surface area of this side is 75x50 $cm^2$. The blue area is (75 - 4 - 4) x (50 - 4 - 4) = 67 x 42 $cm^2$. Don't mind the orange areas, you're not subtracting them twice. You can see that a little more clearly when we cheat a bit and move the blue area:



enter image description here



This is done on a 2D-plane to show the principle, but it holds for 3D volumes as well.






share|cite|improve this answer























  • THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
    – Gabriel Chee
    Aug 1 at 11:52














up vote
1
down vote



accepted










To show why we drop 8 cm on each dimension, let's sketch out one side of the esky*:



enter image description here



(* Not entirely to scale...)



The surface area of this side is 75x50 $cm^2$. The blue area is (75 - 4 - 4) x (50 - 4 - 4) = 67 x 42 $cm^2$. Don't mind the orange areas, you're not subtracting them twice. You can see that a little more clearly when we cheat a bit and move the blue area:



enter image description here



This is done on a 2D-plane to show the principle, but it holds for 3D volumes as well.






share|cite|improve this answer























  • THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
    – Gabriel Chee
    Aug 1 at 11:52












up vote
1
down vote



accepted







up vote
1
down vote



accepted






To show why we drop 8 cm on each dimension, let's sketch out one side of the esky*:



enter image description here



(* Not entirely to scale...)



The surface area of this side is 75x50 $cm^2$. The blue area is (75 - 4 - 4) x (50 - 4 - 4) = 67 x 42 $cm^2$. Don't mind the orange areas, you're not subtracting them twice. You can see that a little more clearly when we cheat a bit and move the blue area:



enter image description here



This is done on a 2D-plane to show the principle, but it holds for 3D volumes as well.






share|cite|improve this answer















To show why we drop 8 cm on each dimension, let's sketch out one side of the esky*:



enter image description here



(* Not entirely to scale...)



The surface area of this side is 75x50 $cm^2$. The blue area is (75 - 4 - 4) x (50 - 4 - 4) = 67 x 42 $cm^2$. Don't mind the orange areas, you're not subtracting them twice. You can see that a little more clearly when we cheat a bit and move the blue area:



enter image description here



This is done on a 2D-plane to show the principle, but it holds for 3D volumes as well.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 1 at 14:43


























answered Aug 1 at 11:24









steenbergh

25017




25017











  • THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
    – Gabriel Chee
    Aug 1 at 11:52
















  • THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
    – Gabriel Chee
    Aug 1 at 11:52















THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
– Gabriel Chee
Aug 1 at 11:52




THANK YOU SO MUCH I AM THE MOST DUMB PERSON EVER BUT THANK YOU I UNDERSTAND
– Gabriel Chee
Aug 1 at 11:52


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