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Math Help - Finding volume and surface area of right prism

  1. #1
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    Question Finding volume and surface area of right prism

    How to find the volume and surface area of right prisms in the attachments ?Finding volume and surface area of right prism-3.jpgFinding volume and surface area of right prism-22.jpgFinding volume and surface area of right prism-11.jpg
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  2. #2
    Senior Member Educated's Avatar
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    \mbox{Volume} = \mbox{Base} * \mbox{Height} * \mbox{Depth}

    \mbox{Surface area (Of each face)} = \mbox{Base} * \mbox{Height}

    Divide the prisms into many simpler shapes (eg. rectangular cubes for volume, or rectangles/squares for surface area) so it is easier to work with and find the surface area and volume seperately. Afterwards add them together to get the final surface area or volume of each prism.

    For the wedge, use:

    \mbox{Volume} = \dfrac{\mbox{Base} * \mbox{Height} * \mbox{Depth}}{2} for the volume

    \mbox{Surface area (Of each triangular face)} = \dfrac{\mbox{Base} * \mbox{Height}}{2} for the surface area of the triangular faces
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  3. #3
    MHF Contributor Unknown008's Avatar
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    I think I'll put more detail for the volume of a prism.

    Volume\ =\ Area\ of\ Cross\ Section\ \times\ Depth

    You need to first identify the cross section of the solid, the area which 'repeats' itself through the solid. In the first one, the cross section is a cross, in the second, it's this 'L' shape and in the last, it's a right angled triangle. Once you get their cross sectiona; area, you'll be able to find the volume by multiplying it by the depth of the solid.
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    For attachment 1 Volume=12*16*20=3840 ?

    and area=12*16=192

    Is this the right answer ?
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    Please solve the 1st one with ur details so that i can understand.
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    Senior Member Educated's Avatar
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    First one:

    \mbox{Total Volume} = (4 * 5 * 3) + (4 * 5 * 3) + (14 * 3 * 4)

    \mbox{Total Volume} = 288~ \mbox{units}^3


    \mbox{Surface Area} = (5*4*(8)) + (4*4*(2)) + (4*3*(4)) + (5*3*(8)) (The single numbers in brackets () are how many faces of each there are.)

    \mbox{Surface Area} = 360~\mbox{units}^2
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  7. #7
    MHF Contributor Unknown008's Avatar
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    The area of the cross can be obtained by dividing the cross into 5 parts; 4 rectangles and 1 central square.

    Each rectangle has area 5*4 = 20.
    Area of 4 rectangles = 20*4 = 80.
    Area of central square = 4*4 = 16.
    Total area of cross section = 16 + 80 = 96.

    Volume of Prism = 96 x 3 = 288 units^3
    Last edited by Unknown008; August 15th 2010 at 02:33 AM. Reason: Did a typo and put units^2 instead of units^3
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  8. #8
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    Very difficult question to understand.
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  9. #9
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    Unit^2 or unit^3 ?
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Oh, sorry, a typo from my part. It's units^3



    Here is a picture to help you understand. The rectangles are reddish and the central square is grey.
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