Question

In your college class, you are taking an advanced construction class. You teacher says you

can build whatever you want, but it has to have a volume of 22 cubic feet. You decide to build a
Pokéball. You decide to build supports sprouting from the center so it can hold its spherical
shape. How long must each support be?

Answer 1

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.