**Module 8 Activity**

Introduction

A theme park company is opening a marine-inspired park in your city. They are in the process of designing the theater where a killer whale show will take place. The following design is already under construction and will house the whales that perform in the show

Main Show Tank Calculation

The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.

Holding Tank Calculation

The holding tanks are congruent in size, and both are in the shape of a cylinder that has been cut in half vertically. The bottom of the tank is a curved surface. What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.

Holding Tank #2 Calculation

In step 1, you found the volume (in cubic feet) of the main tank. If the maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed in the main show tank at any given time? You must explain your answer using words, and you must show all work and calculations to receive credit.

Reflection

1. The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up?

The mock-up is approximately 3 times smaller than volume.

2. Using the information from #4, answer the following question by filling in the blank: The volume of the actual tank is

21985%

of the mock-up of the tank

3. If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?

The shape would be described as a sphere.

I used the formula V = 4/3 π pi πr3 to find the volume of a sphere. Since the problem calls for a quarter-sphere, I divided the volume of a sphere by 4 to find the volume of a quarter-sphere.

To fond the volume of the two tanks, I used the formula V= piπ r2 π h. Since both of the tanks combined equal one whole cylinder, to find the volume of one tank (42390ft ) you simply have to divide the whole number by 2.

To calculate how many whales can be in the tank at once, you must multiply the density of the whales by the volume of the tank: 0.000011142*179503.33= 2

By Adrianna Ringo