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 2 cm squares from each corner and folding up the sides. Let x represent the width of the original piece of cardboard.
Find the width of the original piece of cardboard, x, if the volume of the box is $2496 \mathrm {~cm} ^ { 3 }$ .
A) 27 cm
B) 29 cm
C) 24 cm
D) 28 cm

Question

Quizplus · Accepted Answer

The volume of the box is given by $V = (x-4)(2x-4)(2)$, where $x$ is the width of the cardboard, and $2x$ is the length. After cutting out squares and folding, the dimensions of the box become $x-4$ by $2x-4$ by $2$. Setting $V = 2496$ and solving for $x$ gives $x = 28$ cm.

A Piece of Cardboard Is Twice as Long as It 2496 cm32496 \mathrm {~cm} ^ { 3 }2496 cm3

A Piece of Cardboard Is Twice as Long as It $2496 \mathrm {~cm} ^ { 3 }$