An open box is made from a square piece of sheet metal 19 inches on a side by cutting identical squares from the corners and turning up the sides. Express the volume of the box, V, as a function of the length of the side of the square cut from each corner, x.
A. V(x) = 361x

B. V(x) = (19 - 2x)2

C. V(x) = x(19 - 2x)

D. V(x) = x(19 - 2x)2

Question

An open box is made from a square piece of sheet metal 19 inches on a side by cutting identical squares from the corners and turning up the sides. Express the volume of the box, V, as a function of the length of the side of the square cut from each corner, x. 
 A. V(x) = 361x  
 
 B. V(x) = (19 - 2x)2  
 
 C. V(x) = x(19 - 2x)  
 
 D. V(x) = x(19 - 2x)2

campbell_st · Answer

draw diagram 

|dw:1363981095218:dw|

the dimensions of the area that will be used as the base will be 

length = (19 -2x) 

so the area of the base of the box will be 

$$A = (19 -2x)^2$$

the height of the sides of the box will be x ( the dimension of the cut out )

 Volume = Base area * height 

so $$ V = (19 -x)^2 \times x$$

or 

$$V = x(19 -2x)^2$$