from a 12cm by 12cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box. Express the volume of the box as a function of the length, x, in centimeters.
Type your question in google.
When you see list of result go on :
algebra dot com
To express the volume of the box as a function of the length, we first need to determine the dimensions of the box.
Let's say we cut out squares of side length 'x' from each corner. When the sides are folded up, the length of the resulting box will be (12 - 2x) cm (since we remove 'x' from both sides), and the width will also be (12 - 2x) cm. The height of the box will be 'x' cm, as that is the side length of the squares we cut out.
To calculate the volume of the box, we multiply the length, width, and height:
Volume = (12 - 2x) * (12 - 2x) * x
= (144 - 24x - 24x + 4x^2) * x
= (4x^2 - 48x + 144) * x
= 4x^3 - 48x^2 + 144x
So, the volume of the box can be expressed as a function of the length, x, in centimeters, by the equation:
V(x) = 4x^3 - 48x^2 + 144x