Question

An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic​ feet, what should be the dimensions of the sheet​ metal?

Answer 1

Answer:

24 feet

Step-by-step explanation:

We are given that an open box is to be constructed from a square piece of sheet metal by removing a square side 6 feet from each corner and turning up the edges.

We have to find the dimensions of the sheet metal

Let x feet be the side of square  metal sheet

Length of box=x-12 feet (because 6 feet removed from each corner)

Width of box=x-12 feet

Height of box=6 feet

Volume of box=864 cubic feet

We know that volume of cuboid=$l\times b\times h$

Box is in cuboid shaped

Therefore, volume of box=$6(x-12)(x-12)$

$6(x^2-24x+144)=864$

$x^2-24x+144=\frac{864}{6}$

$x^2-24x+144=144$

$x^2-24x+144-144=0$

$x(x-24)=0$

Then ,$x=0 , x-24=0$

$x=24$

x=0 is not possible because side of square  metal sheet can not be zero

Therefore, x=24

All sides of square metal sheet are equal.

Hence, side of square metal sheet =24 feet