Question

An open box is to be constructed from a square piece of sheet metal by removing a square of side 2 feet from each corner and turning up the edges. If the box is to hold 32 cubic​ feet, what should be the dimensions of the sheet​ metal?

Answer 1

Answer:

length 8 feet and width 8 feet

Step-by-step explanation:

Lets x  be the length and width of the sheet

An open box is to be constructed from a square piece of sheet metal by removing a square of side 2 feet from each corner

so height is 2 feet

length of the box is x-4 feet

width of the box is also x-4 feet

Volume of the box is length times width times height

$V= (x-4)(x-4)2$

$32=2 (x-4)^2$

divide both sides by 2

$16=(x-4)^2$

take square root on both sides

$4=x-4$

Add 4 on both sides

$x=8$

So dimension of the sheet is

length 8 feet and width 8 feet