Related rates: nverted cone has height h=11 inches, radius r=18 inches. Volume is...

1

123Glugh

New member
Joined
May 11, 2018
Messages
2
An inverted cone has a height of [FONT=MathJax_Main]11[/FONT] inches and a radius of [FONT=MathJax_Main]18[/FONT] inches. The volume of the inverted cone is decreasing at a rate of [FONT=MathJax_Main]541[/FONT] cubic inches per second, with the height being held constant. What is the rate of change of the radius, in inches per second, when the radius is [FONT=MathJax_Main]5[/FONT] inches?Round your answer to the nearest hundredth. (Do not include any units in your answer.)
Remember that the volume of a cone is [FONT=MathJax_Math-italic]V[FONT=MathJax_Main]=([/FONT][FONT=MathJax_Main]1/[/FONT][FONT=MathJax_Main]3) [/FONT][FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Math-italic]r[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]h[/FONT].[/FONT]
 
Last edited by a moderator:
123Glugh said:
An inverted cone has a height of [FONT=MathJax_Main]11[/FONT] inches and a radius of [FONT=MathJax_Main]18[/FONT] inches. The volume of the inverted cone is decreasing at a rate of [FONT=MathJax_Main]541[/FONT] cubic inches per second, with the height being held constant. What is the rate of change of the radius, in inches per second, when the radius is [FONT=MathJax_Main]5[/FONT] inches?Round your answer to the nearest hundredth. (Do not include any units in your answer.)
Remember that the volume of a cone is [FONT=MathJax_Math-italic]V[FONT=MathJax_Main]=([/FONT][FONT=MathJax_Main]1/[/FONT][FONT=MathJax_Main]3) [/FONT][FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Math-italic]r[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]h[/FONT].[/FONT]
Click to expand...
What are your thoughts regarding the assignment?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for
 
123Glugh said:
An inverted cone has a height of [FONT=MathJax_Main]11[/FONT] inches and a radius of [FONT=MathJax_Main]18[/FONT] inches. The volume of the inverted cone is decreasing at a rate of [FONT=MathJax_Main]541[/FONT] cubic inches per second, with the height being held constant. What is the rate of change of the radius, in inches per second, when the radius is [FONT=MathJax_Main]5[/FONT] inches?Round your answer to the nearest hundredth. (Do not include any units in your answer.)
Remember that the volume of a cone is [FONT=MathJax_Math-italic]V[FONT=MathJax_Main]=([/FONT][FONT=MathJax_Main]1/[/FONT][FONT=MathJax_Main]3) [/FONT][FONT=MathJax_Math-italic]π[/FONT][FONT=MathJax_Math-italic]r[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math-italic]h[/FONT].[/FONT]
Click to expand...
The volume of the inverted cone is decreasing at a rate of [FONT=MathJax_Main]541[/FONT] cubic inches per second dv/dt = -541in3/sec

height being held constant means h = 11 inches.

What is the rate of change of the radius, in inches per second, when the radius is [FONT=MathJax_Main]5[/FONT] inches means dr/dt = ??in/sec, when r=5in

So what formula do we use to start with?? We have volume and radius and height and the figure is a cone, so use the volume formula for a cone since it has volume, radius and height!

Now do some work and show us that work.
 
media%2F2f4%2F2f4b54e6-8001-4394-8f2e-d436ca83360e%2Fphp7sk7Ea.png
 
You must log in or register to reply here.
Top