An open-topped box is made from a piece of cardboard that is 16 inches by 32 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 210, Figure 4.9, of Ellis/Gulick for a picture). If the side of the squares is x inches, the volume V is the function V = Ax + Bx2 + Cx + D where A = 4 B = -96 C = 512 D If we include the possibility of a volume of 0, then the largest possible value for x is 16 and the smallest possible value for x is 0 To create the box with the largest possible volume, the square must have a length inches. The largest possible volume is 788.275 cubic inches.
An open-topped box is made from a piece of cardboard that is 16 inches by 32 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 210, Figure 4.9, of Ellis/Gulick for a picture). If the side of the squares is x inches, the volume V is the function V = Ax + Bx2 + Cx + D where A = 4 B = -96 C = 512 D If we include the possibility of a volume of 0, then the largest possible value for x is 16 and the smallest possible value for x is 0 To create the box with the largest possible volume, the square must have a length inches. The largest possible volume is 788.275 cubic inches.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter61: Areas Of Circles, Sectors, And Segments
Section: Chapter Questions
Problem 50A
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Transcribed Image Text:An open-topped box is made from a piece of cardboard that is 16 inches by 32 inches by cutting squares of equal size from each corner and bending up the flaps (see p. 210, Figure 4.9, of Ellis/Gulick
for a picture).
If the side of the squares is x inches, the volume V is the function
V = Ax3 + Bx2 + Cx + D
where A = 4
B = -96
C = 512
D = 0
If we include the possibility of a volume of 0, then
the largest possible value for x is 16
and the smallest possible value for x is 0
To create the box with the largest possible volume, the square must have a length
inches.
The largest possible volume is 788.275
v cubic inches.
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