Question

5. Teo cuts 4 squares with side length x in. from the corners of a 10 in. by 15 in.

cardboard rectangle. He folds the remaining cardboard to make

a tray that is x in. high. Write and simplify a function for the volume

V of the tray in terms of x.

HELP

Answer 1

Answer:

• V(x) = 4x³ - 50x² + 150

Step-by-step explanation:

Initial area is 10 in x 15 in.

After cutting the corners and folding, the remaining dimensions are:

• Length, l = 15 - 2x
• Width, w = 10 - 2x
• Height, h = x

The volume of the tray is:

• V = lwh
• V(x) = (15 - 2x)(10 - 2x)x = 4x³ - 50x² + 150