Solve the problem
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 4 cm squares from each corner and folding up the sides. Let x represent the width of the
Original piece of cardboard. Determine a function V that represents the volume of the box in terms
Of x.
A) $V ( x ) = 8 x ^ { 2 }$
B) $V ( x ) = 8 x ^ { 2 } - 96 x + 256$
C) $V ( x ) = 4 x ^ { 2 } - 64 x + 256$
D) $V ( x ) = 8 x ^ { 2 } - 48 x + 64$

Question

Solve the problem
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 4 cm squares from each corner and folding up the sides. Let x represent the width of the
Original piece of cardboard. Determine a function V that represents the volume of the box in terms
Of x. 
A) $V ( x ) = 8 x ^ { 2 }$
B) $V ( x ) = 8 x ^ { 2 } - 96 x + 256$
C) $V ( x ) = 4 x ^ { 2 } - 64 x + 256$
D) $V ( x ) = 8 x ^ { 2 } - 48 x + 64$

Quizplus · Accepted Answer

The volume of the box is given by the product of its length, width, and height. The length of the box is twice the width, so the length is 2x. The width of the box is x. The height of the box is 4 cm. Therefore, the volume of the box is:$$V = lwh = (2x)(x)(4) = 8x^2$$However, we need to subtract the volume of the four corners that were cut out. Each corner has a volume of 4 cm x 4 cm x 4 cm = 64 cm^3. Therefore, the total volume of the four corners is 4 x 64 cm^3 = 256 cm^3.Therefore, the final volume of the box is:$$V = 8x^2 - 256$$

Solve the Problem -A Piece of Cardboard Is Twice as Long

Solve the Problem
-A Piece of Cardboard Is Twice as Long