A spherical storage tank has a diameter of 48 ft and is full of water. How many delivery trucks with cylindrical tanks measuring 8 ft in diameter and 10 ft long can be completely filled from the storage tank?
A)
230 trucks
B)
115 trucks
C)
86 trucks
D)
1152 trucks
Well I determined [B) 115 trucks] to be the answer because:
The Volume of A spherical storage is 57905.83579.
The Volume of a single truck with a cylindrical tank is 502.65482.
so 57905.83579/502.65482=115.200001
round up and it's 115
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To find the number of delivery trucks that can be completely filled from the storage tank, we need to calculate the volume of the spherical storage tank and the volume of each delivery truck, and then divide the tank's volume by the truck's volume.
First, let's calculate the volume of the spherical storage tank.
The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that the diameter of the tank is 48 ft, we can calculate the radius by dividing the diameter by 2: r = 48 ft / 2 = 24 ft.
So, the volume of the spherical storage tank is V = (4/3) * π * (24 ft)^3.
Now, let's calculate the volume of each delivery truck.
The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume, r is the radius, and h is the height.
Given that the diameter of the truck's cylindrical tank is 8 ft, we can calculate the radius by dividing the diameter by 2: r = 8 ft / 2 = 4 ft.
The height of the truck's cylindrical tank is given as 10 ft.
So, the volume of each delivery truck is V = π * (4 ft)^2 * 10 ft.
Now, let's plug in the values and calculate the volumes:
Volume of spherical tank: V = (4/3) * π * (24 ft)^3
Volume of delivery truck: V = π * (4 ft)^2 * 10 ft
We can now divide the volume of the spherical tank by the volume of each delivery truck to find out how many trucks can be completely filled:
Number of trucks = Volume of spherical tank / Volume of delivery truck
Now, performing the calculation:
Number of trucks = [(4/3) * π * (24 ft)^3] / [π * (4 ft)^2 * 10 ft]
Number of trucks = (4/3) * 24^3 / (4^2 * 10)
Simplifying the equation:
Number of trucks = 4 * (24^3 / (4^2 * 10))
Number of trucks = 4 * (13824 / (16 * 10))
Number of trucks = 4 * (13824 / 160)
Number of trucks = 4 * 86.4
So, the number of delivery trucks that can be completely filled from the storage tank is 4 * 86.4, which is approximately 345.6.
Since we cannot have a fraction of a truck, we need to round down to the nearest whole number.
Therefore, the correct answer is C) 86 trucks.