Volume of an open topped box

Question

A square of side x inches is cut out of each corner of a 10 in. by 13 in. piece of cardboard and the sides are folded up to form an open-topped box. A) Write the volume (V) of the box as a function of X

B) Find the domain and range of the function (Thank you in advance, my teacher loves to put nearly this same question on every test, and I never understood it.)

Answer 1

Draw a picture!

 

V = length · width · height

 

x inches is cut from both sides of the length. The new length is 13 - 2x.

x inches is cur from both sides of the width. The new width is 10 - 2x.

The height of the box is x - the side that is folded up.

 

V = (13 - 2x)(10 - 2x)x

V = (130 - 46x + 4x²)x

V = 130x - 46x² + 4x³

V = 4x³ - 46x² + 130x