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26 Μαΐ 2020 · After cutting out the squares from the corners, the width of the open-top box will be 5-2x, and the length will be 7-2x. We’re being asked to maximize the volume of a box, so we’ll use the formula for the volume of a box, and substitute in the length, width, and height of the open-top box.
If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. The quantity we want to optimize is the volume of the box. Let V be the volume of the box. We want to find the maximum value of V.
21 Μαρ 2023 · A closed top box is to be made from piece of cardboard with a surface area of 526. If the volume is maximized, what's the length and width of the box?
If 1200 $cm^2$ of material is available to make a box with a square base and an open top, find the largest possible volume of the box. So I setup my problem like this: $$ x^2 + 4xh = 1200 = P$$ $$x^2 \cdot h = V$$
22 Φεβ 2015 · Let #h# be the height of the box. The surface area of the box is #base + height xx perimeter# #= b^2 + 4bh = 48# From which we can determine: #h = (48 - b^2)/(4b)# The Volume of the box: # V(b) = b^2h = b^2 * ((48 - b^2)/(4b))# # = 12b - (3b^3)/4# The Volume is a maximum when #( d V(b))/ (db) = 0# #(d V(b))/(db) = 12 - (3 b^2)/4 = 0#
Maximizing the Volume of a Box. An open-top box is to be made from a 24 24 in. by 36 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?
In this activity, students will work on a famous math problem exploring the volume of an open box. The aim is to create an open box (without a lid) with the maximum volume by cutting identical squares from each corner of a rectangular card.
