Results 1 to 13 of 13

Math Help - Volume and surface area ?

  1. #1
    Member
    Joined
    Jun 2010
    Posts
    111

    Volume and surface area ?

    Volume and surface area ?-1.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Come on. First, you need the area of the cross section which is a trapezium. How do you find the area of a trapezium?

    Post what you get. We'll try to continue from there.
    Last edited by Unknown008; August 15th 2010 at 02:49 AM. Reason: Added 'which'. I edited before posting and didn't notice that there wasn't much sense in the post.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by haftakhan View Post
    Click image for larger version. 

Name:	1.jpg 
Views:	26 
Size:	65.2 KB 
ID:	18586
    For the volume, the two edges are identical.
    You can cut one off and place it on top of the other.
    This gives you a rectangular block of sides 11, 20, 4.

    The surface area of the front and back sides can be calculated from there.

    Going back to your original drawing, the other sides are 8 by 20, 5 by 20, 14 by 20.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    68
    Quote Originally Posted by Unknown008 View Post
    Post what you get. We'll try to continue from there.
    ...but that's too much work...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Not if the OP understands what to do next
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Jun 2010
    Posts
    111
    Quote Originally Posted by Unknown008 View Post
    Come on. First, you need the area of the cross section which is a trapezium. How do you find the area of a trapezium?

    Post what you get. We'll try to continue from there.
    Area of trapezium=(Mean length of parallel sides/2)*Height b/w parallel sides

    Area={(3+8+3+8)/2}*4

    Area=44

    Is this right ?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Jun 2010
    Posts
    111
    whats the volume now ?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by haftakhan View Post
    Area of trapezium=(Mean length of parallel sides/2)*Height b/w parallel sides

    Area={(3+8+3+8)/2}*4

    Area=44

    Is this right ?
    It should be the exact same as the area of a rectangle + the area of 2 identical triangles,

    which is 4(8)+2(0.5)(3)4=32+12.

    The volume is simplest if you make an 11 by 4 by 20 block, which is 11 by 80 cubic units.
    Otherwise, simply multiply base area by height,
    or front face area by depth, whichever way you want to look at it.

    So, 44 by 20 is ?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Jun 2010
    Posts
    111
    44/20=2.2 unit^2
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by haftakhan View Post
    44/20=2.2 unit^2
    Why are you dividing and why do you have square units ?
    What's volume?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    The surface area is the number of "unit squares" you could place on the surface.

    A unit square has all 4 sides equal to 1 unit in length.
    The surface area of such a square is 1 square unit.

    If you have a rectangular floor 10 meters by 5 meters, how many tiles of surface area 1 square meter
    could you tile the floor with?

    You'd have 10 rows of 5 right?
    Or 5 rows of 10, so you multiply 5 by 10.
    Of course, the corners need to be right-angles.
    However, that's the basis of calculating surface area.

    In your shape, if you cut off one of the triangular edges and place it upside-down on the other edge,
    you will have a rectangular front face of sides 11 and 4 units.
    Therefore, how many unit squares will be on that face ?
    44 right?

    Alternatively, a right-triangle is half a rectangle,
    so we can add up the areas of the two triangles and the rectangle in between.

    Surface area is measured in square units.

    For volume, think in terms of cubes (such as ice cubes or sugar cubes)
    that have all sides 1 unit in length.

    If you have a box of sides 5cm, 2cm and 3cm,
    how many 1 cm sugar cubes could you get inside?
    There will be 5(2)=10 lined up against one face and there will be 3 such rows.
    That's why you multiply all three numbers.

    The units will be cubic units.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Quote Originally Posted by haftakhan View Post
    44/20=2.2 unit^2
    What Archie Meade meant to say when he said:

    So, 44 by 20 is ?
    is to multiply 44 by 20.

    You multiply the area of one face, by the depth to get the volume!
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Member
    Joined
    Apr 2009
    From
    Jerusalem - Israel
    Posts
    108
    volume = [8 x 4 + 2(0.5 x 4 x 3)] x 20
    = ( 32 + 2 x 6) x 20
    = ( 32 + 12) x 20
    = 44 x 20 = 880 cube units

    surface area = (3 + 8 +3) x 20 + 8 x 20 + 2 x (5 x 20) + 2 x 8 x 4 + 4 x (0.5 x 4 x 3)
    = 14 x 20 + 160 + 2 x 100 + 64 + 4 x 6
    = 280 + 160 + 200 + 64 + 24
    = 728 square units.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume & Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 2nd 2009, 02:43 PM
  2. Volume and Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 19th 2009, 12:50 PM
  3. surface area and volume
    Posted in the Geometry Forum
    Replies: 2
    Last Post: October 19th 2008, 10:56 PM
  4. Volume, Surface Area, and Lateral Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 14th 2008, 11:40 PM
  5. Surface area/volume
    Posted in the Geometry Forum
    Replies: 7
    Last Post: August 24th 2006, 11:14 AM

Search Tags


/mathhelpforum @mathhelpforum