the design for a water storage tank calls for a radius of 19.5m and a height of 8.3m each dimension had a variability of +- 0.05m what is the minimum volume of water that the storage tank can hold what is the variability of water most possible and least possible
19.45 <= r <= 19.55
8.25 <= h <= 8.35
1/3 * pi * 19.45^2 * 8.25 = 3268.3
1/3 * pi * 19.55^2 * 8.35 = 3343.0
VERY EASY
To calculate the minimum volume of water that the storage tank can hold, we need to determine the minimum values for the radius and height.
Minimum radius = given radius - variability
Minimum radius = 19.5m - 0.05m = 19.45m
Minimum height = given height - variability
Minimum height = 8.3m - 0.05m = 8.25m
To calculate the volume of a cylinder (water storage tank), we use the formula:
Volume = π * (radius^2) * height
Substituting the minimum values:
Minimum volume = π * (19.45m)^2 * 8.25m
Minimum volume ≈ 31026.60 m^3 (rounded to two decimal places)
To determine the variability of the most and least possible water volumes in the tank, we need to calculate both the minimum and maximum volume values based on the given variability.
Maximum radius = given radius + variability
Maximum radius = 19.5m + 0.05m = 19.55m
Maximum height = given height + variability
Maximum height = 8.3m + 0.05m = 8.35m
Calculating the maximum volume:
Maximum volume = π * (19.55m)^2 * 8.35m
Maximum volume ≈ 32920.07 m^3 (rounded to two decimal places)
Therefore, the minimum volume of water the storage tank can hold is approximately 31026.60 m^3, and the maximum volume is approximately 32920.07 m^3.
The variability of the most possible volume is the maximum volume minus the minimum volume:
Variability of the most possible = Maximum volume - Minimum volume
Variability of the most possible ≈ 32920.07 m^3 - 31026.60 m^3
Variability of the most possible ≈ 1893.47 m^3 (rounded to two decimal places)
The variability of the least possible volume is the minimum volume subtracted from the maximum volume:
Variability of the least possible = Minimum volume - Maximum volume
Variability of the least possible ≈ 31026.60 m^3 - 32920.07 m^3
Variability of the least possible ≈ -1893.47 m^3 (rounded to two decimal places)
Note that a negative variability signifies a decrease from the minimum to maximum values. Therefore, in this scenario, the variability of the least possible volume is -1893.47 m^3 (or a decrease of 1893.47 m^3).