Results 1 to 8 of 8

Math Help - Expanding brackets and calculating perimeter

  1. #1
    Senior Member Mukilab's Avatar
    Joined
    Nov 2009
    Posts
    468

    Expanding brackets and calculating perimeter

    6)Simplify (3g)^3 I couldn't think of an answer for this apart from maybe changing the 3 at the start as because it's 3gx3gx3g so 27g^3?

    7)A square has a semicircle cut out of it. Calculate the perimeter of the shape correct to 3dp. (sides of 12cm)
    Here I got 54.85 which can't be correct because it says caluclate to 3dp. I did the perimeter as perim=piexdiameter. (then halving this to get semi circle etc etc)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jun 2009
    Posts
    61
    1) your answer is correct,
    you can see that also by: (3*g)^3 = 3^3*g^3

    2) i don't understand: what 3dp means?

    if the question is talking about a square with a circle inside that has
    a radius of (square's side/2) than you need to add the square's
    original perimeter and the circle's perimeter.

    that is 48 (square - 12*4) and 12*pi (circle - 2*pi*r)

    if i didn't understand the question correctly please clarify...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Mukilab's Avatar
    Joined
    Nov 2009
    Posts
    468
    Please could you put that into latex? A bit hard to understand that...

    What I did was \text{I added the three sides of the square } 12+12+12=36 \text{ then I added that to } \pi \text{ diameter}

    By DP I mean decimal points
    Last edited by mr fantastic; January 5th 2010 at 01:22 PM. Reason: Fixed the latex the OP wanted to do
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jun 2009
    Posts
    61
    what i meant, again if the question refers to a square with a circle inside,
    which radius is half of the square's side...

    the perimeter is the original perimeter of the square,

    which is 48 (each side 12)

    and in addition the inner perimeter of the circle

    which is 12*pi (the radius - 6, and the perimeter is 2*pi*radius)

    what you still need to to get the decimal representation,

    keeping in mind that pi = 3.1415...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member Mukilab's Avatar
    Joined
    Nov 2009
    Posts
    468
    isn't 2\pi R the area? I'll take it as the perimeter, it's all I really needed.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jun 2009
    Posts
    61
    2\pi r is the perimeter
    \pi r^2 is the area
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,911
    Thanks
    773
    Hello, Mukilab!

    Your answer to #7 is correct! . . . (well, sort of).


    7) A 12-cm square has a semicircle cut out of it.
    Calculate the perimeter of the shape correct to 3 decimal places.
    Code:
                   12
          *-------------------*
          |:::::::::::::::::::|
          |:::::::::::::::::::|
          |:::::::::::::::::::|
       12 |:::::::* * *:::::::| 12
          |:::*           *:::|
          |:*               *:|
          |*                 *|
          |                   |
          *---------*---------*
               6         6

    We want the perimeter of the shaded region.

    A circle has circumference 2\pi r
    The semicircle has perimeter: . \tfrac{1}{2}(2\pi)(6) \:=\:6\pi cm.

    The three sides of the square has perimeter 36 cm.


    The perimeter of the shaded region is: . 6\pi + 36 \;=\;54.84966692 cm.


    Correct to 3 decimal places: . 54.850\text{ cm}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    The problem was not clearly stated.

    It did not specify that the semicircle was on the edge of the square
    . . nor that it was the largest such semicircle.


    In fact, there is a classic problem:
    . . "Find the largest semicircle that can be inscribed in a square".

    The solution looks like this:
    Code:
         o ------*-*-*------o
         |    *::::::::::*. |
         |  *:::::::::::::::*
         | *::::::::::::::* |
         |::::::::::::::*   |
         *::::::::::::*     |
         *::::::::::o       |
         *::::::::*         |
         |::::::*           |
         | *::*             |
         o--*---------------o

    I'll let you work on it . . .

    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member Mukilab's Avatar
    Joined
    Nov 2009
    Posts
    468
    Thanks on the great answer and new problem ^^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help: Expanding Brackets
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 29th 2010, 10:38 AM
  2. expanding brackets
    Posted in the Algebra Forum
    Replies: 6
    Last Post: February 27th 2010, 04:51 AM
  3. expanding brackets
    Posted in the Algebra Forum
    Replies: 5
    Last Post: January 8th 2010, 07:30 PM
  4. expanding brackets
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 8th 2008, 11:07 AM
  5. expanding brackets
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 19th 2008, 04:38 PM

Search Tags


/mathhelpforum @mathhelpforum