To find the quadratic equation that best models the volume of the box, let's start by noting the given dimensions and the expression for the volume of a rectangular box.
1. The height of the box [tex]\( h \)[/tex] is given as [tex]\( h \, \text{cm} \)[/tex].
2. The length [tex]\( l \)[/tex] of the box is given as [tex]\( 10 \, \text{cm} \)[/tex].
3. The width [tex]\( w \)[/tex] of the box is given as twice the height, so [tex]\( w = 2h \)[/tex].
The formula for the volume [tex]\( V \)[/tex] of a rectangular box is given by multiplying the length, width, and height:
[tex]\[ V = l \cdot w \cdot h \][/tex]
Substituting the given dimensions into the volume formula, we have:
[tex]\[ l = 10 \, \text{cm} \][/tex]
[tex]\[ w = 2h \][/tex]
Now, substitute [tex]\( l \)[/tex] and [tex]\( w \)[/tex] into the volume formula:
[tex]\[ V = 10 \cdot (2h) \cdot h \][/tex]
Next, simplify the expression:
[tex]\[ V = 10 \cdot 2h \cdot h \][/tex]
[tex]\[ V = 20h \cdot h \][/tex]
[tex]\[ V = 20h^2 \][/tex]
Therefore, the quadratic equation that best models the volume of the box is:
[tex]\[ V = 20h^2 \][/tex]
This matches the given choices and confirms that the correct answer is:
[tex]\[ V = 20 h^2 \][/tex]
So, the quadratic equation which best models the volume of the box is [tex]\( V = 20 h^2 \)[/tex].
