Results 1 to 2 of 2

Math Help - [SOLVED] Prism and Cylinder

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    222

    [SOLVED] Prism and Cylinder

    Hey,

    This is on page 19 # 32 of the Barron's SAT Math II Book.

    If a square prism is inscribed in a right circular cylinder of radius 3 and height 6, the volume inside the cylinder but outside the prism is

    a) 2.14
    b) 3.14
    c) 61.6
    d) 115.6
    e)169.6

    Can you please show the steps cuz i really dont get this question. Thanks in advance!!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,859
    Thanks
    741
    Hello, fabxx!

    If a square prism is inscribed in a right circular cylinder of radius 3 and height 6,
    the volume inside the cylinder but outside the prism is:

    . . (a)\;2.14\qquad(b)\;3.14 \qquad (c)\;61.6 \qquad (d)\;115.6 \qquad (e)\;169.6

    Visualize a right circular cylinder (a soup can).
    A square-based block is fitted into the can snugly.
    They both have the same height, 6.

    The base looks like this:
    Code:
                  * * *
              *           *
            o - - - - - - - o
           *|             / |*
            |           /   |
          * |         /     | *
          * |     6 /      x| *
          * |     /         | *
            |   /           |
           *| /     x       |*
            o - - - - - - - o
              *           *
                  * * *

    The diameter of the circle is 6.
    Let x = side of the square.

    From Pythagorus: . x^2+x^2\:=\:6^2 \quad\Rightarrow\quad 2x^2 \:=\:36
    . . x^2 \:=\:18\quad\Rightarrow\quad x \:=\:\sqrt{18} \:=\:3\sqrt{2}


    The volume is the cylinder is: . V_1 \;=\;\pi r^2h \;=\;\pi(3^2)(6) \;=\;54\pi

    The volume of the block is: . V_2 \;=\;LWH \;=\;(3\sqrt{2})(3\sqrt{2})(6) \;=\;108


    Solution: . 54\pi - 108 \;\approx\;61.6 . . . answer (c)

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Volume of a cylinder
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2010, 10:34 AM
  2. [SOLVED] cylinder & blueprint
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 8th 2010, 03:17 AM
  3. Replies: 5
    Last Post: September 24th 2009, 11:43 AM
  4. Right Prism
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 22nd 2008, 10:29 PM
  5. Prism
    Posted in the Geometry Forum
    Replies: 1
    Last Post: August 4th 2008, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum