Explanation Given data: y Riley is holding an ice cream cone on a hot summer day that melts and ice cream drops down through a small hole at the vertex of the cone. The solid ice cream cone has height 5 inches and the radius 2 inches. The melted ice cream is dripping at a rate .05 cubic inch per minute. The rate of change of the height of the ice cream is required when its height is 3 inches. Method/Formula used: The volume of the cone of height h and base radius r is V = 1 3 π r 2 h . Calculation: The solid ice cream cone has height 5 inches and the radius 2 inches shown in figure here. The melted ice cream is dripping at a rate .05 cubic inch per minute. We find the rate of change of the height of the ice cream is required when its height is 3 inches. Let α be the semi vertical angle of the cone, then tan α= h r = 5 2 . Let r ' be the radius of the cone when its height is 3 inches, then tan α= h r = 5 2 ⇒ r = 2 5 h . Now, volume of the cone is V = 1 3 π r 2 h = 1 3 π ( 2 5 h ) 2 h ⇒ V = 4 75 π h 3

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.5, Problem 57A

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To find: The rate change of height of the ice cream cone when its radius is 3 inches.

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Chapter 3.5, Problem 56A

Chapter 3.5, Problem 58A

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The rate change of height of the ice cream cone when its radius is 3 inches.

Solution Summary: The author calculates the rate of change of the height of an ice cream cone when its radius is 3 inches.

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To find: The rate change of height of the ice cream cone when its radius is 3 inches.

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Chapter 3 Solutions