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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The equation that can be used to determine the volume of the sphere is 4/3π10³
<h3>What is the volume of the sphere?</h3>
A sphere is a three-dimensional object in which points from its center to its circumference is equidistant.
Volume of a sphere = 4/3πr³
Where:
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The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed
Step-by-step explanation:
Given
Distance = d = 45 miles
Time = t = 3/4 hour
The unit rate is defined as the distance per unit time. In this case, the unit rate can also be called speed.
So,
Using this unit rate we can see if the car can travel 65 miles in 1.25 hours or not
Given
Distance = d1 = 65 miles
Speed = s = 60 miles per hour
Putting the values in the formula for speed
As we can see that 1.08 is less than 1.25 so the driver will reach the meeting before time if he drives on a constant speed of 60 miles per hour
Hence,
The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed
Keywords: Speed, unit rate
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Im pretty sure tge answers -1.68426
Answer:
4.28 ounces each
Step-by-step explanation:
21.4 divided by 5 equals 4.28
