Answered: The radius of a cone is decreasing at a…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter10: Exponential And Logarithmic Functions

Section10.CT: Test

Problem 21CT

See similar textbooks

Related questions

Question

The radius of a cone is decreasing at a constant rate of 8 feet per minute. The volume remains a constant 54 cubic feet. At the instant when the height of the cone is 66 feet, what is the rate of change of the height? The volume of a cone can be found with the equation V=13πr2h.V=31πr2h. Round your answer to three decimal places.

Expert Solution

Step 1

Let the radius of cone is r feet and it’s height

Be h feet.

Then given that its radius is decreasing at a constant rate 8 feet/minute

And its volume V = 54 feet³

Then at h= 66 feet, we have to find dh/dt

Since volume af cone v = 1/3πr²h

When r = 54, h = 66 then

54 = π/3r²(66)

Πr²/3 = 54/66
r² = 54/66 x 3/π = 0.78
r =0.884 feet

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions