SOLUTION: How many square inches of material is needed to create an open top rectangular solid volume is 54 cubic inches? Assume that the length and width are of the same measurement and tha

Question 1180964: How many square inches of material is needed to create an open top rectangular solid volume is 54 cubic inches? Assume that the length and width are of the same measurement and that the height is twice the length
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the volume is 54 cubic inches.
formula for volume is l * w * h
l = length
w = width
h = height
length and width are the same, therefore l = w
let s = l = w, therefore volume = s^2 * h
the height is equal to twice the length, therefore h = 2s
volume now equals 2s * s^2 which becomes volume = 2s^3
since volume = 54, then 54 = 2s^3
divide both sides of this eqution by 2 to get:
27 = s^3
solve for s to get:
s = 3 because 3^3 = 27
since h = 2s, then h = 6
measurements of the rectangular solid are 54 = l * w * h = 6 * 3 * 3 = 54.
the rectangular solid has an open tope.
the box will require the following square inches of material.
1 bottom * 3 * 3 = 9 square inches.
4 sides * 6 * 3 = 72 square inches.
total square inches of material required is 81 square inches.

i double checked my figures and they look correct.
let me know if you agree.

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