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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.) 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.

the equation given to solve this is v=4/3 pi radius by the power of 3

Respuesta :

The given radius is = 60 feet

The volume of the sphere is given by = [tex]\frac{4}{3} \pi r^{3}[/tex]

So we will find the volume of the sphere using radius as 60 and pi as 3.14

Volume = [tex]\frac{4}{3}*3.14*60*60*60[/tex] = 902059.20 cubic feet

As quarter of anything is defined as its one-fourth part, so here the volume of the quarter of sphere can be calculated by finding one fourth of the calculated volume.

So volume of quarter sphere = [tex]\frac{902059.20}{4}[/tex]

= 225514.80 cubic feet

And rounding this to nearest whole number we get 225515 cubic feet as the answer.


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