100 Points Math Question
1). The main show tank has a radius of 70 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). 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 35 feet and the height of tank #2 is 120 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 one-sixth 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 #3, 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.
Please show equations and explain in words
