This question boils down to this: "What is the diagonal of a square with a side length of 90 ft?"
The key to this question is the properties of squares. All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles. Now we have two triangles, each with angle measures of 45°, 45°. and 90°. (an isoceles right triangle)
This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!
In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
The formula for volume of a sphere is V=(4pi*r^3)/3. Plugging in 12 for r we get V=(4pi*(12)^3)/3 V=(4pi*1728)/3 V=(6912pi)/3 V=2304pi Round to 2 decimal places: 7238.23 Final Answer: 7238.23 cubic units. Hope I helped :)
