Answer:
2√3
Step-by-step explanation:
You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).
The magnitude of R is 2√3.
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In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...
Sin = Opposite/Hypotenuse
sin(30°) = √3/R
R = √3/sin(30°) = √3/(1/2) = 2√3
Of course, doing this on your calculator will give a numerical answer, which you may not want.
Answer:
The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.
Step-by-step explanation:
A gallon equals 0.134 cubic feet. First, we determine the amount of water (), measured in cubic feet, needed to put out the fire under the assumption that water is consumed at constant rate:
(1)
Where:
- Volume rate, measured in feet per minute.
- Time, measured in minutes.
If we know that and
, then the amount of water is:
And the diameter of the cylindrical tank based on the capacity found above is determined by volume formula for a cylinder:
(2)
Where:
- Diameter, measured in feet.
- Height, measured in feet.
If we know that and
, then the minimum diameter is:
The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.