An inverted cone has a height of 15 mm and a radius of 16 mm. The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant. What is the rate of change of the radius, in mm per second, when the radius is 6 mm?Round your answer to the nearest hundredth. (Do not include any units in your answer.)Remember that the volume of a cone is V=1/3 πr2 h.

Question
Asked Mar 18, 2019

An inverted cone has a height of 15 mm and a radius of 16 mm. The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant. What is the rate of change of the radius, in mm per second, when the radius is 6 mm?

Round your answer to the nearest hundredth. (Do not include any units in your answer.)

Remember that the volume of a cone is V=1/3 πr2 h.

check_circleExpert Solution
Step 1

The volume of a cone is V=1/3 πr2 h

The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant. 

dV / dt = 1/3 πh.d(r2)/dt as h is held constant and hence dh/dt = 0

Step 2

Fnd the formula for the rate of change of the volume, in mm per second.

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Step 3

To find the rate of change of the radius, in mm per second, when the radius is 6 mm.

Here&...

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Math

Calculus