Thank you for visiting The outer diameter of a spherical tank measures 6 feet If the tank is made with a material 3 4 inches thick estimate the volume. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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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