My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 30th, 2016, 01:03 PM   #1
Newbie
 
Joined: Oct 2016
From: Toronto

Posts: 3
Thanks: 0

Question about related rate

A downward cone is melting. Assume that the radius r and the height h always satisfy h = 6r. The radius r, height h, and slant height L.

1. Express l as a function of r.
L(r)= sqrt((6pi^2)+r^2) is this correct?

2 Find a formula for the lateral surface area A as a function of r.
La(r)= pi*r*L is this correct?

3. Find a formula for the volume V as a function of the slant height L.
V(L)= La + pi*r^2 is this correct ?

4. Suppose that the lateral surface area is decreasing at a constant rate of 30pi mm2/hr. Find an equation which gives dr/dt in terms of r.
How do I do this question?

5. At what rate is the radius changing when r = 300mm?
Apple11 is offline  
 
October 30th, 2016, 01:13 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,638
Thanks: 1474

Quote:
Originally Posted by Apple11 View Post
A downward cone is melting. Assume that the radius r and the height h always satisfy h = 6r. The radius r, height h, and slant height L.

1. Express l as a function of r.
L(r)= sqrt((6pi^2)+r^2) is this correct?
where would $\pi$ come in?

$L = \sqrt{r^2 + h^2} = \sqrt{r^2 + (6r)^2} = \sqrt{37r^2} = r\sqrt{37}$

$L(r) = \sqrt{37}r$

Quote:
2 Find a formula for the lateral surface area A as a function of r.
La(r)= pi*r*L is this correct?
They want you to express this solely as a function of $r$.

Use the fact that $h=6r$ to express $L$ as a function of $r$ (i.e. problem 1)

Quote:
3. Find a formula for the volume V as a function of the slant height L.
V(L)= La + pi*r^2 is this correct ?
you've got $r$'s in your formula. That's not allowed.

find the formula for the volume of a cone in $r$ and $h$ and then use the results of (1) and $h=6r$ to convert that formula into one solely in terms of $L$

Quote:
4. Suppose that the lateral surface area is decreasing at a constant rate of 30pi mm2/hr. Find an equation which gives dr/dt in terms of r.
How do I do this question?

5. At what rate is the radius changing when r = 300mm?
get 1-3 correct first and we'll go on to 4 and 5

Last edited by romsek; October 30th, 2016 at 01:15 PM.
romsek is offline  
October 30th, 2016, 05:40 PM   #3
Newbie
 
Joined: Oct 2016
From: Toronto

Posts: 3
Thanks: 0

Quote:
Originally Posted by romsek View Post
where would $\pi$ come in?

$L = \sqrt{r^2 + h^2} = \sqrt{r^2 + (6r)^2} = \sqrt{37r^2} = r\sqrt{37}$

$L(r) = \sqrt{37}r$



They want you to express this solely as a function of $r$.

Use the fact that $h=6r$ to express $L$ as a function of $r$ (i.e. problem 1)



you've got $r$'s in your formula. That's not allowed.

find the formula for the volume of a cone in $r$ and $h$ and then use the results of (1) and $h=6r$ to convert that formula into one solely in terms of $L$



get 1-3 correct first and we'll go on to 4 and 5
2 Find a formula for the lateral surface area A as a function of r.
La(r)= pi*r*L --> pi*r*r*sqrt(37) --> pi*r^2*sqrt(37)
Is this correct ?

3. Find a formula for the volume V as a function of the slant height L.
The volume of the cone is 1/3*pi*r^2*h. I don't understand how to do next.
Apple11 is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
question, rate, related



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
plz Help me: Related rate latzi Calculus 1 July 25th, 2009 06:07 AM
Related Rate titans4ever0927 Algebra 2 February 25th, 2009 06:15 PM
Related Rate titans4ever0927 Calculus 1 February 25th, 2009 11:48 AM
Another pre-related rate question squeeze101 Algebra 2 October 31st, 2008 04:10 PM
related rate mangox Calculus 9 October 25th, 2008 02:50 PM





Copyright © 2019 My Math Forum. All rights reserved.