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. You must explain your answer using words, and you must show all work and calculations to receive credit. 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? 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 sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?

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.

1. Volume = 5128.67 ft³

The volume if sphere is given by:

V = (4/3)πr³

If the tank is cut into half vertically, then the volume of sphere becomes.

V = (4/3)πr³ / 2

If the tank is cut into half again horizontally, then the volume of the sphere becomes.

V = (4/3)πr³ / 4

Hence, as the main tank forms a quarter sphere, its Volume is given by:

V = (4/3)πr³ / 4

It is given in the question that the radius is 70 ft.

Substitute that in the given formula:

V = (4/3)π(70)³ / 4

V = 5128.67 ft³

 2. Volume of tank = 461,814 ft³

Step-by-step explanation:

Congruent tanks implies that both tanks are of identifical shape, form & dimensions. Congruent means that the tanks have the same radius as well as height. Hence, the heights and radii of tanks #1 and #2 are equal and the same.

Let's list out the information given us:

radius(tank #1) = 35 ft ⇒ radius(tank #2) = 35 ft, height(tank #2) = 120 ft ⇒ height(tank #2) = 120 ft

Volume of cylinder = πr²h

The tanks have been cut into half, as such:

Volume of tank = ½πr²h

Volume of tank = Volume(tank #1) + Volume(tank #2)

Since the tanks are congruent (same dimensions), we have:

⇒ ½πr²h + ½πr²h ⇒ πr²h

Volume of tank =  π * 35² * 120 = 147,000 π

Volume of tank = 461,814 ft³

3.  1047.2 ft³

Step-by-step explanation:

The following information is missing:

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)

The only dimension needed for the main show tank is its radius. Then the model radius will be 1/6 * 60 = 10 feet

The volume of a sphere is:

V = 4/3 * π * r³

For a quarter sphere it is:

V = 4/3 * π * r³ * 1/4

V = 1/3 * π * r³

For the smaller mock-up tank:

V = 1/3 * π * 10³

V = 1047.2 ft³

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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