Cut out a sector S with an angle 0 radians (where 0 < 0 < 2)...

 

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Cut out a sector S with an angle 0 radians (where 0 < 0 < 2) from a circle with a radius of 1, and use this sector to form a conical cup T. In other words, the lateral surface of T is made from sector S. Let h be the depth of cup T, and r be the radius of the circle at the top. 0 1 1 r T To determine the value of 0 that maximizes the volume V of cup answer the following questions: (a) Express V in terms of r of h. (b) Express h in terms of r. T (f) Determine the value of 0 that maximizes V. (c) Express V in terms of r. (d) Determine the value of r that maximizes V. (e) Express in terms of r. 4 201- Cut out a sector S with an angle 0 radians (where 0 < 0 < 2) from a circle with a radius of 1, and use this sector to form a conical cup T. In other words, the lateral surface of T is made from sector S. Let h be the depth of cup T, and r be the radius of the circle at the top. 0 1 1 r T To determine the value of 0 that maximizes the volume V of cup answer the following questions: (a) Express V in terms of r of h. (b) Express h in terms of r. T (f) Determine the value of 0 that maximizes V. (c) Express V in terms of r. (d) Determine the value of r that maximizes V. (e) Express in terms of r. 4 201-

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To find the angle theta that maximizes the volume V of the conical cup T we ... View the full answer