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 shape tank? Round your answer to the nearest whole number. You must explain your answer using words and you must show all your work and calculations to receive credit
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Given:
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.
To find:
What is the volume of the quarter-sphere shape tank?
Solution:
From given, we have,
The radius of spherical shape tank = 70 feet.
Volume of the sphere = 4/3 × π × r³
= 4/3 × 22/7 × 70³
= 1437333.3 feet³
Quarter of the sphere = Volume/4
= 1437333.3/4
= 359333.33 feet³
1 Cubic Foot = 7.48051948 Gallons
∴ 359333.33 feet³ = 359333.33 feet³ × 7.48051948 Gallons
= 2688000 gallons.
Therefore, the volume of the quarter-sphere shape tank is 2688000 gallons.
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