Question

I'm working on a writing assignment right now, I'm looking for someone to check my work as I go along to make sure I'm on the right track.

This is the first problem -
""You are making boxes and begin with a rectangular piece of cardboard that measures 1.75 meters by 1.25 meters. From each corner of that rectangular piece you cut out a square piece that is 0.25 meter on a side, as shown. You fold up the "flaps" to form a box without a lid.

What is the outside surface area of the box?
What is its volume?"

Answer 1

Rest of the question -
"If the corner cuts were squares 0.3 meter on a side, would the resulting box have a larger or smaller volume than the first box?
What is your estimate of the size of the square corner cuts that will give a box with the largest volume?""

Answer 2

And here is my work for the first two questions --

surface area of a rectangular prism = 2lw + 2lh + 2wh
In this case we'd subtract .25 x 2 from the length to account for each "flap", so length would be 1.25 m.
Do the same thing for width, so width would be .75 m.
Then, since this box has no lid, we need to alter the surface area formula to being
lw + 2lh + 2wh
then substitute in values and solve -
(1.25 x .75) + 2(1.25 x .25) + 2(.75 x .25)

= 1.9375 meters squared for surface area

For volume,
volume of a rectangular prism is given by the formula - lwh
substitute values and solve
(1.25)(.75)(.25)
=
.234375 cubic meters

How does this look so far?

Answer 3

but when you are calculating surface area don't forget to minus the pieces that are cut out

Answer 4

Ah sorry, I forgot to attach the image -

Answer 5

Wouldn't these already be "cut out" since it is being folded up into a rectangular prism/box?

Answer 6

Everything looks fine to me \[\checkmark\]

Answer 7

Thank you!