Question

!!!WILL MARK BRAINLIEST IF CORRECT AND ALL PARTS OF THE QUESTION ANSWERED!!!!

1. 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.

(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.

Answer 1

(a) The dimensions of the base of the box are (8 -2x) and (10 -2x). The depth of the box is x. The volume is the product of these dimensions.
  V = x(8 -2x)(10 -2x)

(b) A graphing calculator is suitable "technology". The process is ...
• write the equation in the calculator
• adjust the scaling so the curve fills the display area
• select the maximum point to reveal its coordinates

The value of x that maximizes box volume is about 1.5 inches.