# A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides. Write an equation for the volume V of the box in terms of x?

##### 2 Answers
May 13, 2018

The volume of this box will be $4 x \left(5 - x\right) \left(4 - x\right)$ while $x \le 4$.

#### Explanation:

We are constructing a right rectangular prism, with the dimensions $10 - 2 x$ by $8 - 2 x$ by $x$.

The volume of this box will be the product of its dimensions or $\left(10 - 2 x\right) \left(8 - 2 x\right) x = 4 x \left(5 - x\right) \left(4 - x\right)$ but $x \le 4$.

May 13, 2018

Length of the box $L = 8 - 2 x$ in

Width of the box $W = 10 - 2 x$ in

Height of the box $H = x$ in

Volume of the box

$V = L \times W \times H = \left(10 - 2 x\right) \left(8 - 2 x\right) x {\text{ ""in}}^{3}$

where $x < 4$ in