To determine the length of the supports, we first need to determine the dimensions of the Pokéball. Since a Pokéball is a sphere, we know that its volume can be calculated using the formula:
V = (4/3)πr^3
where V is the volume and r is the radius.
Since the volume is given as 22 cubic feet, we can solve for r:
22 = (4/3)πr^3
r^3 = (22*3)/(4π)
r = 1.91 feet
Next, we need to determine the length of the supports. Since they will be perpendicular to the base of the Pokéball, they will form a right triangle with the radius of the sphere as the hypotenuse. We can use the Pythagorean theorem to solve for the length of the supports:
a^2 + b^2 = c^2
where c is the radius of the sphere and a and b are the lengths of the supports.
Solving for a or b, we get:
a = sqrt(c^2 - b^2)
or
b = sqrt(c^2 - a^2)
Since we want the supports to be the same length, we can set a = b and solve for that length:
a^2 + b^2 = c^2
2a^2 = r^2
a = sqrt(r^2/2)
Plugging in r = 1.91 feet, we get:
a = sqrt(1.91^2/2) = 1.35 feet
Therefore, each support must be 1.35 feet long.