An entertainment company is opening a theme park in a nearby city. They are in the process of designing the theatre where a water show will take place. The following design is already under construction and will house the dolphins that perform in the show

1.) The main show tank has a radius of 70 feet and forms a quarter-sphere. What is the volume of the quarter-sphere shaped 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.

2.) The holding tanks (there are two of them) 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 35 feet and the height of tank #2 is 125 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.

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 eight of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank? (Show all steps to receive full credit.)

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. (Show all steps to receive full credit.)

1) = 20510 ^3ft (volume of the quarter sphere.)

2) = 240406 ^3ft each or 240406. 25^3 ft, (480812.5 ^3 ft combined volume of half vertically cut cylinder tanks)

3) =2564.^3ft  or 2563.69225^3ft (volume of smaller m/u tank)

4) The volume of the original main show tank is 87.5% of the mock-up of the tanks volume meaning difference in increase.

Step-by-step explanation:

1)  4/3 pi x r+r

= 1.333 x 3.14 x 70 x 70

= 4.18562 x 70 x 70 = 20509.538

2) We (x2) dimensions not radius to make 1 whole cylinder

r = 35 feet = stays same as radius can only be half of a joined circle,

then vertically cut

h = 125 x 2 = 250ft

Equation = for Area first

Pi x r ^2

= 3.14ft x 35r x 35r = Surface Area = 3846.5

Volume = Surface area x H

= 3846.5 x 125 = = 480812.5 combined.

= 480812.5 / 2 = each = 240406.25ft

3) 1/8 of 20509.538 = 2563.69225

4) 7/8 of 20509.538 =2563.69225 x 7 = 17945.84575

For the larger tank the increase is 17946 ft rounded up (0.165 value) of that of the smaller mock up tank. Therefore percentage 1/8 = 12.5% and 7/8 = 87.5%

We multiply by the increase 08.75 or multiple 2563.69225 x 7 to find answer of 17945.84575 this is labelled increase size difference. We then just add ^3(power)ft to show the volume in answer format.

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.