Results 1 to 5 of 5

Math Help - Volume is smaller than area of base. Why? I thought this wasn't possible.

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    19

    Volume is smaller than area of base. Why? I thought this wasn't possible

    Let f and g be the functions given by f(x) = 1+sin(2x) and g(x) = ex/2. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g as shown in the figure above.

    a. Find the area of R.

    b. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y = f(x) to y = g(x). Find the volume of this solid.

    I am not asking anyone to answer these two questions; I have solved them and I got the correct answers, but I don't understand why my answers are correct. The answer to part a is BIGGER than the answer to part b. How can this be true? The area of the base can't be bigger than the volume of the solid??

    Please help. Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: Volume is smaller than area of base. Why? I thought this wasn't possible

    Quote Originally Posted by nicksbyman View Post
    Let f and g be the functions given by f(x) = 1+sin(2x) and g(x) = ex/2. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g as shown in the figure above.

    a. Find the area of R.

    b. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y = f(x) to y = g(x). Find the volume of this solid.

    I am not asking anyone to answer these two questions; I have solved them and I got the correct answers, but I don't understand why my answers are correct. The answer to part a is BIGGER than the answer to part b. How can this be true? The area of the base can't be bigger than the volume of the solid??

    Please help. Thanks
    Enclosed in what figure?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    19

    Re: Volume is smaller than area of base. Why? I thought this wasn't possible

    Quote Originally Posted by Prove It View Post
    Enclosed in what figure?
    Sorry I don't know how to post the figure. I think that you don't need the figure to answer the question though.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2

    Re: Volume is smaller than area of base. Why? I thought this wasn't possible

    The statement "area is bigger than volume" is nonsense, since you are comparing things with different dimensions.

    Is 1 foot the same as 1 inch (or 1 liter) because they both have the same number?

    A sphere with radius 1 unit will have surface area of 4pi units^2, and a volume of (4/3)pi units^3...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,427
    Thanks
    1857

    Re: Volume is smaller than area of base. Why? I thought this wasn't possible

    Perhaps you are thinking that "volume= base times height". Don't forget that the height can be less than 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: February 13th 2011, 12:36 PM
  2. Wasn't sure where this was supposed to go..
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: August 27th 2009, 05:07 AM
  3. Replies: 1
    Last Post: February 5th 2009, 05:17 PM
  4. Replies: 1
    Last Post: December 3rd 2008, 10:43 PM
  5. Replies: 2
    Last Post: October 20th 2008, 04:32 AM

Search Tags


/mathhelpforum @mathhelpforum