Question

The company is building a scale model of the theater's main show tank for an investor's presentation. Each dimension will be made 1/6 of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?

Answer 1

This means the mock-up tank has a volume 216 times smaller than the initial tank.

Explanation:

The ratio between volume is given by

`(V_2)/(V_1)=((1/6)L^(3) )/(L^(3))  =(1)/(216)`

This means the mock-up tank has a volume 216 times smaller than the initial tank.

Answer 2

1047.2 ft³

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