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The spheres cost $2 per square foot and Selim can spend $20 per sphere. What is the maximum diameter of the spheres he can purchase?

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The surface area of a sphere is 4πr2, where r is the radius of the sphere. The cost of a sphere is 2 per square foot, so the cost of a sphere with radius r is 8πr2. Selim can spend 20 per sphere, so he can purchase a sphere with radius r such that 8πr2≤20. This inequality can be solved for r to get r≤8π20​​=2π5​​. The diameter of a sphere is 2r, so the maximum diameter of the spheres Selim can purchase is 22π5​​=10π​≈3.162 feet.

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