Thread: Weird Geometry Problem

Any insight on this one?

Given: 1. Sphere with diameter = 3 inches
2. Lateral edge of the square pyramid inside of the sphere is 2 inches
and the base is 2 inches

Find: If you made 100 of these items, how many gallons of solution are
needed to fill the voids?

Hint: [1 ft = about 7.5 gallons]

does anyone know how to do this one?

Use
V = 4/3 * Pi * r^3 for sphere
V = 1/3 * a^2 * h for pyramid where a is the length of the base.
You get,
Volume of Sphere = 4/3 * Pi * (3/2)^3
Volume of Pyramid = 1/3 * 4 * h

Now you need h, use the formula (1) here http://mathworld.wolfram.com/SquarePyramid.html

You should get h = root(2), so
Volume of Pyramid = 4/3 * root(2)

Now,
Volume of void = Volume of sphere - Volume of pyramid
Total number of gallons required is 100 * Volume of void.