Solve the problem.
-From a 18-inch by 18-inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express
The volume of the box as a function of x.
A) $V ( x ) = 4 x ^ { 3 } - 72 x ^ { 2 }$
B) $V ( x ) = 4 x ^ { 3 } - 72 x ^ { 2 } + 324 x$
C) $V ( x ) = 2 x ^ { 3 } - 54 x ^ { 2 }$
D) $V ( x ) = 2 x ^ { 3 } - 54 x ^ { 2 } + 18 x$

Question

Solve the problem.
-From a 18-inch by 18-inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express
The volume of the box as a function of x. 
A) $V ( x ) = 4 x ^ { 3 } - 72 x ^ { 2 }$
B) $V ( x ) = 4 x ^ { 3 } - 72 x ^ { 2 } + 324 x$
C) $V ( x ) = 2 x ^ { 3 } - 54 x ^ { 2 }$
D) $V ( x ) = 2 x ^ { 3 } - 54 x ^ { 2 } + 18 x$

Quizplus · Accepted Answer

After cutting out squares of side length x from each corner, the dimensions of the box will be (18-2x) by (18-2x) by x. The volume, V(x), is therefore $V(x) = x(18-2x)(18-2x) = x(324-72x+4x^2) = 4x^3 - 72x^2 + 324x$.

Solve the Problem V(x)=4x3−72x2V ( x ) = 4 x ^ { 3 } - 72 x ^ { 2 }V(x)=4x3−72x2

Solve the Problem $V ( x ) = 4 x ^ { 3 } - 72 x ^ { 2 }$