Question

please help and if you can thank you so much Main Show Tank Calculation: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? Roundyour answer to the nearest whole number. You must explain your answer sing words, and you must show all work and calculations to receivecredit.Holding Tank Calculations: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 curvedsurface 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 is120 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 made1/6 of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?5. Using the information from #4, 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.

Answer 1

359,007 cubic feet

Explanations:

1) The formula for calculating the volume of the spherical tank is expressed as:

`V=(4)/(3)\pi r^3`

where:

r is the radius of the tank

The volume of the quarter-sphere shaped tank is expressed according to the formula

`\begin{gathered} V=((4)/(3)\pi r^3)/(4) \\ V=(4)/(12)\pi r^3 \\ V=(1)/(3)\pi r^3 \end{gathered}`

Substitute the value for the radius as shown below

`\begin{gathered} V=(1)/(3)\pi(70)^3 \\ V=(1)/(3)*3.14*343000 \\ V=359006.66ft^3 \\ V\approx359,007ft^3 \end{gathered}`

Therefore the volume of of the quarter-sphere shaped tank to the nearest whole number is 359,007 cubic feet