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A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminum with squares of length x (in inches) removed from each corner. Then the flaps are folded up to form an open box. a. Show that the volume of the box is given by V(x) = 4x – 108x + 720x for 0

A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminum with squares of length x (in inches) removed from each corner. Then the flaps are folded up to form an open box. a. Show that the volume of the box is given by V(x) = 4x – 108x + 720x for 0

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.10: Problems Without Solutions
Problem 12P
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A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminum with squares of length x (in inches) removed from each corner. Then the flaps are folded up to form an open box. a. Show that the volume of the box is given by V(x) = 4x – 108x + 720x for 0<x< 12. b. Graph the function from part (a) and use a "Maximum" feature on a graphing utility to approximate the length of the sides of the squares that should be removed to maximize the volume. Round to the nearest tenth of an inch. c. Approximate the maximum volume. Round to the nearest cubic inch. 24 in. x: 30 in. 24 – 2x 30 – 2x
Transcribed Image Text:A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminum with squares of length x (in inches) removed from each corner. Then the flaps are folded up to form an open box. a. Show that the volume of the box is given by V(x) = 4x – 108x + 720x for 0<x< 12. b. Graph the function from part (a) and use a "Maximum" feature on a graphing utility to approximate the length of the sides of the squares that should be removed to maximize the volume. Round to the nearest tenth of an inch. c. Approximate the maximum volume. Round to the nearest cubic inch. 24 in. x: 30 in. 24 – 2x 30 – 2x
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