write and solve an equation to find the width of the box if its volume is 96 cubic centimeters. Then find its surface area

Answer 1

volume = 96 cubic centimeters = 96 cm^3

equation is LW^2 =96 or W^2L = 96

or if a cube with L=W then W^3 = 96, W = cube root of 96

IF the box is a cube then a side of the box = s will = the cube root of 96

= about 4.58 centimeters

surface area = 6 times the area of one side = about 6 x (4.58)^2 = about 125.8 cm^2

but if it's not a cube, just a rectangular 3 D box, then the surface area could be anywhere from 125.8 to an infinitely large area. The width could be anywhere between 0 and infinity.

still 96 is a slightly supicious number, suggesting there may be more information in the problem such as possibly the length and width are integers.

V=LW^2 or WL^2.=96

maybe 4 by 4 by 6, then Width = 4 cm, with Surface Area = 32+4(24) = 128 cm^2

or 72+64 = 138 cm^2

or 2 by 8 by 6, then Width = 2 cm with Surface Area = 8 + 4(48) = 200 cm^2

or 64+ 4(16) = 128 cm^

or 1 by 1 by 96, then Width = 1, with Surface Area = 2 +4(96) = 386 cm^2

best guess: 128 cm^2 with width = either 4 or 2, assuming by "width" you mean the shortest length of a side of the box

but endless other possibilities if the edge is not an integer. Some more information is needed to narrow down the solution.

96 = W^2L then W=sqr(96/L) and Surface Area = A = 2W^2 + 4WL

or 96 = L^2W then W = 96/L^2 and Surface Area = A = 2L^2 +4LW