Question

An open box is constructed from a square 10-inch piece of cardboard by cutting squares of length x inches out of each corner and folding the sides up. Express the volume of the box as a function of x, and state the domain.

Answer 1

Answer: V = 8x^3-80x^3 +200x

Domain 0<x<5

Step-by-step explanation:

Dimension of cardboard = 10 by 10

Let the length of box = 10-2x

Let the width of box = 10 - 2x

Let the height of box be =x

Volume = l×w×h

V = (10-2x)×(10-2x)×x

V= 100 - 40x +42 × x

V= 8x^3 -80x^2 +200x

Answer 2

The volume of the box as a function of x is 8x³ - 80x² + 200x

The formula to calculate volume will be:

= Length × Width × Height

The dimensions of the cardboard will be:

Length = 10 - 2x

Width = 10 - 2x

Height = x

Therefore, the volume will be:

= (10 - 2x) × (10 - 2x) × x

= 8x³ - 80x² + 200x

Therefore, the volume of the box as a function of x is 8x³ - 80x² + 200x.

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