Question

1. Main Show Tank Calculation:

The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number.

2. Holding Tank Calculations:

The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 30 feet and the height of tank #2 is 110 feet?

3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made ⅛ of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?

4. Using the information from #4, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.

Answer 1

1. a quarter is a fourth. the volume of a sphere = (4/3)πr³
So the volume of the tank would be = (1/4)(4/3)π(60)³
= (1/3)π(60)³
= 72,000π ft³
2. The holding tanks are half cylinders. Combined they make a whole cylinder. volume of a cylinder is area of circle times length.
volume tank 1&2 = (110)π(30)²
= 99,000π ft³
3. radius of main show tank goes from 60 real tank to 60/8 = 7.5 mock-up tank
= (1/3)π(7.5)³
= 140.625 ft³
4. 72,000/140.625 * 100 = 51,200%
essentially 8³ * 100
very high since you are looking at % real tank to model tank