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Math Help - Help with surface area, volumes and measures

  1. #1
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    Help with surface area, volumes and measures

    Hello is there anyone who can help me out with these questions, i would really appreciate it. Thanks

    Q1. Work out the surface area of this triangular prism which has a cross-section in the shape of an equilateral triangle of side 6cm and a length of 12cm.


    Q2. 8400mm(squared) to cm(squared)
    Q3. 2.5cm(cubed) to mm(cubed)


    Q4 If a,b,c,r and h represent lengths, use dimensions theory to deduce whether each of these expressions is length,area,volume or none of these.

    a) abc
    b) 2thirdsbc
    c) 3bh + πr
    d) 5h(squared)a
    e) a + πb
    f) ab(squared) + r(squared)
    g) a(b+2r)
    h) halfπr(squared)h
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  2. #2
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    Quote Originally Posted by sammyfox07 View Post
    Hello is there anyone who can help me out with these questions, i would really appreciate it. Thanks

    Q1. Work out the surface area of this triangular prism which has a cross-section in the shape of an equilateral triangle of side 6cm and a length of 12cm.


    Q2. 8400mm(squared) to cm(squared)
    Q3. 2.5cm(cubed) to mm(cubed)


    Q4 If a,b,c,r and h represent lengths, use dimensions theory to deduce whether each of these expressions is length,area,volume or none of these.

    a) abc
    b) 2thirdsbc
    c) 3bh + πr
    d) 5h(squared)a
    e) a + πb
    f) ab(squared) + r(squared)
    g) a(b+2r)
    h) halfπr(squared)h
    To Q1:

    Let s denote the side of an equilateral triangle then the area of the triangle is calculated by:

    a_{eT} = \frac14\cdot s^2 \cdot \sqrt{3}

    The surface area consists of 2 triangles (base and top) and 3 rectangles whose length is the height of the prism and whose width is the side of the triangle.
    Now it's your turn.

    I've got a_{p} \approx 247.18\ cm^2

    to Q2:
    Use the ratio: 1\ cm^2 = 100\ mm^2

    to Q3:
    Use the ratio: 1\ cm^3 = 1000\ mm^3

    to Q4:

    You know that the volume V=lll and the area a = ll

    a) abc ....... lll~\rightarrow~V
    b) 2thirdsbc ....... ll~\rightarrow~a ....... \frac23 is a constant without a dimension!
    c) 3bh + πr ....... This one is really funny because you add a length ( \pi r) to an area... So I assum that there is a typo and you probably meant 3bh + \pi r^2
    d) 5h(squared)a ....... lll~\rightarrow~V ...... (Do you see why?)

    I'll leave the rest for you:

    e) a + πb
    f) ab(squared) + r(squared)
    g) a(b+2r)
    h) halfπr(squared)h
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