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?

volume of a sphere = (4/3)pi(r^3)

we know that r = 24

volume of cylinder = pi(r^2(h)
we know r = 4, h = 10

then divide volume of sphere by volume of cylinder

48

To find out how many delivery trucks with cylindrical tanks can be filled from the storage tank, we need to determine the volume of the storage tank and the volume of each delivery truck, and then divide the storage tank volume by the truck volume.

1. Volume of the storage tank:
The storage tank is spherical, and we can use the formula for the volume of a sphere to find its volume.
V = (4/3) * π * r^3
where V is the volume, π is a mathematical constant (approximately 3.14159265), and r is the radius. Since we are given the diameter, we need to divide it by 2 to get the radius.
Given diameter = 48 ft
Radius = 48 ft / 2 = 24 ft
V = (4/3) * π * 24^3
V ≈ 72411.84 cubic feet

2. Volume of each delivery truck:
The delivery truck tank is cylindrical, and we can use the formula for the volume of a cylinder to find its volume.
V = π * r^2 * h
where V is the volume, π is a mathematical constant (approximately 3.14159265), r is the radius, and h is the height.
Given diameter = 8 ft
Radius = 8 ft / 2 = 4 ft
Height = 10 ft
V = π * 4^2 * 10
V ≈ 502.65 cubic feet

3. Calculate the number of trucks that can be filled:
Now, we can divide the volume of the storage tank by the volume of each truck to find the number of trucks that can be completely filled.
Number of trucks = V_storage / V_truck
Number of trucks = 72411.84 / 502.65
Number of trucks ≈ 144

Therefore, approximately 144 delivery trucks with cylindrical tanks measuring 8 ft in diameter and 10 ft long can be completely filled from the storage tank.