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Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.

Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 57AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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1. Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2. 2. A tank of water in the shape of a cone is leaking water at a constant rate of 2ft°/hour. The base radius of the tank is 5 ft and the height of the tank is 14 ft. At what rate is the depth of the water in the tank changing when the depth of the water is 6 ft? And at what rate is the radius of the top of the water in the tank changing when the depth of the water is 6 ft?
Transcribed Image Text:1. Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2. 2. A tank of water in the shape of a cone is leaking water at a constant rate of 2ft°/hour. The base radius of the tank is 5 ft and the height of the tank is 14 ft. At what rate is the depth of the water in the tank changing when the depth of the water is 6 ft? And at what rate is the radius of the top of the water in the tank changing when the depth of the water is 6 ft?
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