(a)
To express: The volume of the box in terms of
(a)
Explanation of Solution
Given information: Square corners cuts out of pieces of metal that measure
Calculation:
The diagram of a metal sheet that measure
Figure (1)
So, the box from metal sheet can be made as:
Figure (2)
The box is in the shape of a cuboid. So, use the formula to calculate volume of cuboid is:
To find the volume in terms of x , substitute
Therefore the volume of the box in terms of x is
(b)
To find: The maximum volume of the box to the nearest tenth of cubic inch.
(b)
Answer to Problem 3E
The maximum volume of the box to the nearest tenth is
Explanation of Solution
Given information: Square corners cuts out of pieces of metal that measure
Calculation:
From part (a), the volume of the box is:
Now, differentiate the
Equate the function to zero.
Again differentiate the function to find the maximum.
The function given negative value for
Therefore, the maximum volume of the box to the nearest tenth is
(c)
To find: The length, width, and height of the box to nearest tenth.
(c)
Answer to Problem 3E
The length of the box is 11.6 in, breath is 4.6 in and height is 1.7 in.
Explanation of Solution
Given information: Square corners cuts out of pieces of metal that measure
Calculation:
From part (b), the maximum volume of the box is
So, the height of the box is 1.7 in.
The length of the box is:
The breath of the box is:
Therefore, the length of the box is 11.6 in, breath is 4.6 in and height is 1.7 in.
Chapter 12 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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