how do I find the max number of 1.7 inch diameter spheres that can be stored in a cylindrical tank the tank has a radius of 2 inches and height of 4 inches there are 2
inches of water in the tank
what difference does it make how much water is in the tank?
Are we to assume maximal packing, or just a rectangular lattice of spheres?
To find the maximum number of 1.7 inch diameter spheres that can be stored in a cylindrical tank, we need to calculate the available space in the tank and then find out how many spheres can fit into that space.
First, let's calculate the available height of the tank after considering the 2 inches of water:
Available height = Total height of the tank - Height of water
Available height = 4 inches - 2 inches
Available height = 2 inches
Next, let's calculate the available volume of the tank:
Available volume = π * (tank radius)² * (available height)
Available volume = π * (2 inches)² * (2 inches)
Available volume = 8π cubic inches
Now, let's find out the volume of each sphere:
Volume of a sphere = (4/3) * π * (sphere radius)³
The diameter of the sphere is given as 1.7 inches, so the radius will be half of that:
Sphere radius = 1.7 inches / 2
Sphere radius = 0.85 inches
Volume of a sphere = (4/3) * π * (0.85 inches)³
Volume of a sphere ≈ 2.997 cubic inches (approx.)
Finally, we can calculate the maximum number of spheres that can be stored in the tank by dividing the available volume of the tank by the volume of each sphere:
Max number of spheres = Available volume / Volume of a sphere
Max number of spheres = 8π cubic inches / 2.997 cubic inches
Max number of spheres ≈ 8.79 (approx.)
Therefore, the maximum number of 1.7 inch diameter spheres that can be stored in the cylindrical tank is approximately 8.