Question

A 7ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 37 ft^3. find the side length of the original cube

Answer 1

Let s = side length of cube

Answer 2

the original cube has a volume of V = s^3

Answer 3

The part you cut off that is 7 ft high has a volume of 7s^2, since you multiply height by area of the base

Answer 4

So

Volume of Remaining Piece = (Original Volume) - (Volume of Cut Off Piece)

Volume of Remaining Piece = (s^3) - (7s^2)

37 = s^3 - 7s^2

0 = s^3 - 7s^2 - 37

s^3 - 7s^2 - 37 = 0

I'll let you finish

Answer 5

im confused

Answer 6

where are you stuck

Answer 7

how to get the side from what you have said

Answer 8

well the best way to solve s^3 - 7s^2 - 37 = 0 is to use a graphing calculator to approximate the root

Answer 9

you can't solve this exactly (not easily anyway)

Answer 10

if you don't have a graphing calculator, you can use wolfram alpha

http://www.wolframalpha.com/input/?i=s^3+-+7s^2+-+37+%3D+0