  # 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

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?

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.

Step 3

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

Here&...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

### Calculus 