Answer:
[tex]Volume = 2x^{3}-4x^{2}[/tex]
Step-by-step explanation:
Let x be the width of the jewellery box
Given:
Length of the box is twice its width
Length of the box = [tex]2\times width[/tex]
Length of the box = [tex]2\times x= 2x[/tex]
depth of the box is equal to 2 inches less than its width.
depth of the box = [tex]width-2[/tex]
depth of the box = [tex]x-2[/tex]
The volume of the box is 64 inches.
Solution:
We know that the formula of the volume is.
[tex]Volume = length\times width\times depth[/tex]
Now we substitute all known value in above.
[tex]Volume = 2x\times x\times (x-2)[/tex]
[tex]Volume = 2x^{2}(x-2)[/tex]
[tex]Volume = 2x^{3}-4x^{2}[/tex]
Therefore, the equation of the volume of the box is.
[tex]Volume = 2x^{3}-4x^{2}[/tex]
