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Math Help - surface areas and volumes

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    surface areas and volumes

    a cylinder has total surface area of 42cm square,it has a curved surface area which is 1/3of total surface area.find volume of cylinder?
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    Quote Originally Posted by anjana View Post
    a cylinder has total surface area of 42cm square,it has a curved surface area which is 1/3of total surface area.find volume of cylinder?
    The surface of a cylinder has three pieces: two end-caps with area (pi)r^2 and one rectangle that is wrapped around the cylinder which has area C*h where C is the circumference of the end-cap and h is the height of the cylinder. So the SA of the cylinder is
    SA = 2(pi)r^2 + 2(pi)rh
    The volume of the cylinder is
    V = (pi)r^2 * h

    So. The curved surface has an area of (1/3)*(42 cm) = 2(pi)rh.
    We need r and h and we only have one equation. We need another.

    Well, SA = 42 cm = 2(pi)r^2 + 2(pi)rh.

    The first equation gives us a value of rh:
    rh = (1/3)*(42)/[2(pi)] = 2.22817 cm^2 or so.

    We can insert this value into the second equation:
    42 = 2(pi)r^2 + 2(pi)(2.22817)

    We can solve this for r. I get r = 2.11100 cm or so.

    Now we can find h, since we know the value of rh and r:
    h = (rh)/r = 1.05550 cm or so.

    Now:
    V = (pi)r^2 * h = 14.77703 cm^3 or so.

    -Dan
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