SOLUTION: I am having trouble solving this problem. Thank you in advance!!!
An open wooden box is a cube with side x cm. The box, including its bottom, is made of wood that is 1 cm thic
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-> SOLUTION: I am having trouble solving this problem. Thank you in advance!!!
An open wooden box is a cube with side x cm. The box, including its bottom, is made of wood that is 1 cm thic
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Question 125857This question is from textbook Introductory Algebra
: I am having trouble solving this problem. Thank you in advance!!!
An open wooden box is a cube with side x cm. The box, including its bottom, is made of wood that is 1 cm thick. Find a polynomial for the interior volume of the cube.
This is what I have come up with:
Volume=volume of large solid – volume of small solid
(xcm)(xcm)(xcm) = xcm^3 (large solid)
(xcm)(xcm)(1cm)(5)= 5(xcm^2- 1cm) small solid
xcm^3 - 5(xcm^2 * 1cm)
This question is from textbook Introductory Algebra
You can put this solution on YOUR website! Here's the way I see this!
The volume of the outside of the box is simply: as you have noted.
For the volume of the inside, note that the sides of the interior are 2x cm. less than the sides of the exterior, right? That's cm for each side of the interior.
The height of the interior is 1 cm less than the height of the exterior because the box is open and there is no cover on the top. So the interior height is cm.
The volume of the interior then is:
I think that what you have found (or perhaps trying to find) is the volume of the 1 cm-thick material from which the box is constructed.
To find the volume of the interior of the box, one need only to multiply the three interior dimensions of length, width, and height.
And, as noted above, the interior length and the interior width are both 2 cm less than the exterior dimensions while the interior height is only 1 cm less than the exterior height.
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