The largest possible volume of the given box is; 96.28 ft³
<h3>How to maximize volume of a box?</h3>
Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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Answer:
the answer is 2.25
Step-by-step explanation:
you divide 6.75÷ 3
Answer:
1. slope
2.Positive
3.up and down
4. Left and right
5. 1/1 or over 1 up 1
Step-by-step explanation:
Answer: 16 5/8
Step-by-step explanation:
3 1/2 = 7/2
4 3/4 = 19/4
7/2 * 19/4 = 133/8 or 16 5/8
