Results 1 to 4 of 4

Thread: Related Rates with Spheres

  1. #1
    Newbie
    Joined
    Apr 2017
    From
    St. Paul
    Posts
    2

    Related Rates with Spheres

    Here's the question I have:

    The radius of a sphere is increasing at a constant rate of 2cm/sec. At the instant when the volume of the sphere is increasing at 32pi cm^3/sec, the surface area of the sphere is

    A) 8pi
    B) 32pi/3
    C) 16pi
    D) 64pi
    E) 256pi/3

    So far I have dr/dt=2, and when dv/dt=32, SA=?

    V=4/3pir^3
    SA=4pir^2

    I'm not sure how to relate these two equations. I assume I would solve for the radius of the sphere first, by finding the derivative of the Volume equation: dv/dt=4pir^2dr/dt, but I don't know what to do after that.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,107
    Thanks
    3647

    Re: Related Rates with Spheres

    Given ...

    $\dfrac{dr}{dt}=2 \, cm/sec$, $\dfrac{dV}{dt} = 32\pi \, cm^3/sec$

    $\dfrac{dV}{dt} = \color{red}{4\pi r^2} \cdot \dfrac{dr}{dt}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,364
    Thanks
    2681
    Awards
    1

    Re: Related Rates with Spheres

    Quote Originally Posted by Velmahr View Post
    Here's the question I have:

    The radius of a sphere is increasing at a constant rate of 2cm/sec. At the instant when the volume of the sphere is increasing at 32pi cm^3/sec, the surface area of the sphere is

    A) 8pi
    B) 32pi/3
    C) 16pi
    D) 64pi
    E) 256pi/3

    So far I have dr/dt=2, and when dv/dt=32, SA=?

    V=4/3pir^3
    SA=4pir^2

    I'm not sure how to relate these two equations. I assume I would solve for the radius of the sphere first, by finding the derivative of the Volume equation: dv/dt=4pir^2dr/dt, but I don't know what to do after that.
    $\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}=32\pi $ solve for $r$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,340
    Thanks
    2859

    Re: Related Rates with Spheres

    \frac{dV}{dt}= \frac{d((4/3)\pi r^3)}{dt}= \frac{d((4/3)\pi r^3)}{dr}\frac{dr}{dt}= (4\pi r^2)(2).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rates and Related rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 12th 2016, 09:25 PM
  2. Related Rates 2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 27th 2010, 01:42 PM
  3. related rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 19th 2008, 09:57 AM
  4. Rates and Related Rates!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 2nd 2008, 10:53 AM
  5. rates and related rates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 29th 2007, 09:51 PM

Search Tags


/mathhelpforum @mathhelpforum