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.
Accepted Solution
A:
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