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Vika [28.1K]
2 years ago
8

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive an

y points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise The radius of a right circular cone is increasing at a rate of 1.7 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 185 in. and the height is 134 in.? Part 1 of 4 The volume of a cone with base radius r and height h is given by V = 1 3 πr2h. To find the rate of change of the volume, we need to find dV dt . By the Chain Rule, we know that dV dt = ∂V ∂ Incorrect: Your answer is incorrect. dr dt + ∂V ∂ Incorrect: Your answer is incorrect. dh dt .
Mathematics
1 answer:
Gekata [30.6K]2 years ago
3 0

Answer:

Step-by-step explanation:

The volume of a cone is expressed as shown;

V = πr²h/3

The rate of change of volume is expressed as;

dV/dt =  ∂V/dr * dr/dt +  ∂V/dh * dh/dt

dV/dr is the rate of change of volume with respect to radius

∂V/dh is the rate of change of volume with respect to height

dr/dt is the rate of change in radius = 1.7 in/s

dh/dt is the rate of change in height = 2.2 in/s

∂V/∂r = 2πrh/3

if r = 185 and h = 134

∂V/∂r = 2π(185)(134)/3

∂V/∂r = 51, 893.73 in²

Also  ∂V/∂h =  πr²/3

if h = 134 in

 ∂V/∂h  =  π(134)²/3

∂V/∂h  =  π(134)²/3

∂V/∂h = 18,793.95in²

Substitute the given values into the differential equation above

dV/dt =  ∂V/dr * dr/dt +  ∂V/dh * dh/dt

dV/dt =  51, 893.73 *(1.7) + 18,793.95 *(2.2)

dV/dt =  88,219.341 + 41,346.68

dV/dt = 129,566.021 in³/s

Hence the volume of the cone is changing at 129,566.021 in³/s

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