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The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 159 in. and the height is 112 in.? Step 1 The volume of a cone with base radius r and height h is given by V = 1½πr²h. To find the rate of change of the volume, we need to find dv By the Chain Rule, we know that dt av av dv dt a r dr + dt dh მ h dt h Step 2 dr dh We are given that 1.9 and -2.4. dt dt av Also, Step 3 ar 를 trh and ah =|༤ av Πρ 3 3 When r = 159 and h 112, then av av and ər ah Submit Skip (you cannot come back)

The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 159 in. and the height is 112 in.? Step 1 The volume of a cone with base radius r and height h is given by V = 1½πr²h. To find the rate of change of the volume, we need to find dv By the Chain Rule, we know that dt av av dv dt a r dr + dt dh მ h dt h Step 2 dr dh We are given that 1.9 and -2.4. dt dt av Also, Step 3 ar 를 trh and ah =|༤ av Πρ 3 3 When r = 159 and h 112, then av av and ər ah Submit Skip (you cannot come back)

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 8A
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The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 159 in. and the height is 112 in.? Step 1 The volume of a cone with base radius r and height h is given by V = 1½πr²h. To find the rate of change of the volume, we need to find dv By the Chain Rule, we know that dt av av dv dt a r dr + dt dh მ h dt h Step 2 dr dh We are given that 1.9 and -2.4. dt dt av Also, Step 3 ar 를 trh and ah =|༤ av Πρ 3 3 When r = 159 and h 112, then av av and ər ah Submit Skip (you cannot come back)
Transcribed Image Text:The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 159 in. and the height is 112 in.? Step 1 The volume of a cone with base radius r and height h is given by V = 1½πr²h. To find the rate of change of the volume, we need to find dv By the Chain Rule, we know that dt av av dv dt a r dr + dt dh მ h dt h Step 2 dr dh We are given that 1.9 and -2.4. dt dt av Also, Step 3 ar 를 trh and ah =|༤ av Πρ 3 3 When r = 159 and h 112, then av av and ər ah Submit Skip (you cannot come back)
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