Question

part 5 of 5
a box is to be made out of a
rectangular piece of cardboard that is
12 inches wide and 16 inches long.
squares x inches on a side are cut out
of the corners and the sides are bent
upwards.
16 in.
12 in.
the width of the box is $12-2x$ in. (type an expression using x as the variable.)
the height of the box is $x$ in. (type an expression using x as the variable.)
b. write a simplified expression for the volume of the box.
the volume of the box is $x^3 - 56x^2 + 192x$ $in^3$.
(type an expression using x as the variable.)
c. write a simplified expression for the outside surface area of the box. (note that the box does n
the outside surface area of the box is $square$ $in^2$.
(type an expression using x as the variable.)
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Explanation:

Step1: Find original cardboard area

$\text{Area} = 16 \times 12 = 192$

Step2: Subtract cut-out square areas

There are 4 squares, each area $x^2$. Total cut area: $4x^2$.
$\text{Surface Area} = 192 - 4x^2$

Answer:

$192 - 4x^2$