Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.
1 answer:
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Answer:
Volume of the tank = 636 ft³
Step-by-step explanation:
Formula for the volume of a cylinder is,
V = πr²h
Where r = radius of the cylinder
h = height of the cylinder
By substituting the values of radius and height of the water tank given in the question,
V =
= 202.5π
= 202.5 × (3.14)
= 635.85 ft³
≈ 636 ft³
Therefore, volume of the cylindrical water tank is 636 ft³.
Answer:
26 ft square by 13 ft high
Step-by-step explanation:
The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...
2·(8788 ft^3) = (26 ft)^3
The square bottom of the tank is 26 ft square, and its height is 13 ft.
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<em>Solution using derivatives</em>
If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...
x^2 + 4x(8788/x^2) = x^2 +35152/x
The derivative of this is zero when area is minimized:
2x -35152/x^2 = 0
x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576
x = 26
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As the attached graph shows, a graphing calculator can also provide the solution.
