Explanation:
To determine the number of football helmets that can fit into a shed that is 20 x 10 ft, we need to calculate the shed's total volume and divide it by the volume of an average-sized football helmet. Let's assume the average-sized football helmet has a cylindrical shape.
The volume of a cylinder can be calculated using the formula: V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder's base, and h is the height of the cylinder.
First, let's calculate the shed's volume:
Shed Volume = Length × Width × Height
Shed Volume = 20 ft × 10 ft × (1/3 or 1/4) ft
Next, let's calculate the volume of an average-sized football helmet. Since you mentioned that they are average-sized, we'll assume a typical shape for a football helmet, which is somewhat similar to a prolate spheroid.
The volume of a prolate spheroid can be calculated using the formula: V = (4/3)πa²b, where V is the volume, π is a mathematical constant approximately equal to 3.14159, a is the semi-major axis (half of the longer axis), and b is the semi-minor axis (half of the shorter axis).
Since the exact dimensions of an average-sized football helmet were not provided, I'll assume approximate values for the semi-major axis (a) and semi-minor axis (b) based on typical football helmet proportions. Let's assume a = 6 inches (0.5 ft) and b = 5 inches (0.417 ft).
Football Helmet Volume = (4/3) × π × a² × b
Finally, we can calculate the number of football helmets that can fit into the shed by dividing the shed volume by the volume of an average-sized football helmet:
Number of Football Helmets = Shed Volume / Football Helmet Volume