A company wants to design a box with four rectangular sides and a square top and bottom. a) Letting a denote the length of one of the sides of the bottom of the box, and letting y denote the height of the box, sketch a picture of the box, labeling the length, width, and height. The company wants to use exactly 100 cm² of material for the box. That is, the box's surface area will be equal to 100 cm?. Write an equation in terms of æ and y representing this constraint, putting the variables on the left side. cm? Solve for y to find y as a function of r. y = b) Using your work from part (a), write a formula for the volume of the box, V(r), as a function of æ. Simplify as much as possible. V(z) = c) Use an online source to approximate the maximum value of V(x) on the interval [0, 10]. What a value corresponds to this maximum value? What does this mean in the context of the problem? A. This is the length of the side of the box that produces the maximum volume of a box with a surface area of 100 cm?. OB. This is the maximum volume of a box with a surface area of 100 cm?. OC. This is the area of the base of the box that produces the maximum volume of a box with a surface area of 100 cm?.

A company wants to design a box with four rectangular sides and a square top and bottom. a) Letting a denote the length of one of the sides of the bottom of the box, and letting y denote the height of the box, sketch a picture of the box, labeling the length, width, and height. The company wants to use exactly 100 cm² of material for the box. That is, the box's surface area will be equal to 100 cm?. Write an equation in terms of æ and y representing this constraint, putting the variables on the left side. cm? Solve for y to find y as a function of r. y = b) Using your work from part (a), write a formula for the volume of the box, V(r), as a function of æ. Simplify as much as possible. V(z) = c) Use an online source to approximate the maximum value of V(x) on the interval [0, 10]. What a value corresponds to this maximum value? What does this mean in the context of the problem? A. This is the length of the side of the box that produces the maximum volume of a box with a surface area of 100 cm?. OB. This is the maximum volume of a box with a surface area of 100 cm?. OC. This is the area of the base of the box that produces the maximum volume of a box with a surface area of 100 cm?.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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