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Answer :
Final answer:
The spherical tank with an outer diameter of 6 feet and a material thickness of 3/4 inches can hold approximately 106 cubic feet of water.
Explanation:
Solution:
The first step in solving this problem is translating the diameter of the tank into the radius, which is required to calculate the volume of a sphere. The radius can be calculated by dividing the diameter by two: so we have 3 feet as the radius of the tank. However, the tank has a thickness of material (here 3/4 inches), which we should subtract from the outer radius to get the inner radius. To maintain the same measurement unit (which here is in terms of feet), we first convert 3/4 inches into feet: 3/4 inches = 0.0625 feet. Therefore, the inner radius of the tank becomes 3 - 0.0625 = 2.9375 feet.
The volume of the tank (ignoring the thickness of the tank) can be calculated by the formula of volume of a sphere, which is 4/3*π*r³. When we substitute the radius into the formula, we get 4/3*π*(2.9375)³ = approximately 106 cubic feet
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