Volume of a Box A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure). (a) Find a function that models the volume of the box. (b) Find the values of x for which the volume is greater than 200 in?. (c) Find the largest volume that such a box can have. 20 in. 12 in.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.2: Polynomial Functinos And Their Graphs
Problem 89E: Volume of a Box An open box is to constructed from a piece of cardboard 20 cm by 40 cm by cutting...
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In the problem you are asked to find a function that models a real life-life situation and then use the model to answer questions about the situation. 

 

Volume of a Box A box with an open top is to be constructed from a rectangular piece
of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each
corner and then folding up the sides (see the figure).
(a) Find a function that models the volume of the box.
(b) Find the values of x for which the volume is greater than 200 in?.
(c) Find the largest volume that such a box can have.
20 in.
12 in.
Transcribed Image Text:Volume of a Box A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure). (a) Find a function that models the volume of the box. (b) Find the values of x for which the volume is greater than 200 in?. (c) Find the largest volume that such a box can have. 20 in. 12 in.
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