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  1. #1
    mets9131
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    SAT problem help

    For Pre calc cannot figure this out even though I know it is simple

    A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high

    A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high

    There is no overlap

    A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
    B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain
    C. If a shett 11 X 17 inches paper was used to make a cylinder 17 inches tall, how would its volume and surface area compare to the volume and surface area of the 8 1/2 inch tall cylinder? Explain
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    Quote Originally Posted by mets9131 View Post
    For Pre calc cannot figure this out even though I know it is simple

    A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high

    A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high

    There is no overlap

    A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
    B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain
    I shall answer the first two.

    A.) The same since the area of the sheet is the same in both the cylinders the surface area is the same.

    B.)The volume of the short cylinder is,
    V=(1/3)pi(5.5)^2(8.5)=269.26 cubic inches

    The volume of the tall cyclinder is,
    V=(1/3)pi(4.25)^2(11)=208.065 cubic inches

    Thus the shorter has more volume.
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  3. #3
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    Quote Originally Posted by mets9131 View Post
    For Pre calc cannot figure this out even though I know it is simple

    A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high
    the it is rolled along its long side!

    Quote Originally Posted by mets9131 View Post
    A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high
    the it is rolled along its short side!

    Quote Originally Posted by mets9131 View Post
    There is no overlap

    A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
    B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain
    C. If a shett 11 X 17 inches paper was used to make a cylinder 17 inches tall, how would its volume and surface area compare to the volume and surface area of the 8 1/2 inch tall cylinder? Explain
    Hi,

    to A) Look at THP's reply.

    to B) The taller cylinder has the height 11". You have to calculate the radius of the circle at the ground of the cylinder first:

    c = 2*pi*r, thus 8.5" = 2*pi*r. Therefore: r ≈ 1.353"

    v = pi*r^2*h, thus: v ≈ pi * (1.353")^2 * 11". Therefore v ≈ 63.244 cubic inches

    The smaller cylinder has the height 8.5". You have to calculate the radius of the circle at the ground of the cylinder first:

    c = 2*pi*r, thus 11" = 2*pi*r. Therefore: r ≈ 1.751"

    v = pi*r^2*h, thus: v ≈ pi * (1.751")^2 * 8.5". Therefore v ≈ 81.845 cubic inches

    So the higher cylinder has the smaller volume.

    EB
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    Quote Originally Posted by ThePerfectHacker View Post
    ...

    A.) The same since the area of the sheet is the same in both the cylinders the surface area is the same.

    ...
    Hi,

    I need some help here: In my opinion the area of the circles of the bottom and the top of a cylinder belong to the surface too.

    For my reply I have taken over your approach, but I'm not certain ... so please enlight me.

    EB
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    Quote Originally Posted by earboth View Post
    Hi,

    I need some help here: In my opinion the area of the circles of the bottom and the top of a cylinder belong to the surface too.
    I did not chose to include that for the two circles are not created from the paper itself.
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  6. #6
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    Quote Originally Posted by ThePerfectHacker View Post
    I did not chose to include that for the two circles are not created from the paper itself.
    Hi,

    thank you for this explanation, but...

    According to my dictionary the sheet of paper must be the "curved surface". Therefore I believe that the (complete) surface of a cylinder contains the curved surface and two circles.
    But maybe the definition of "surface of a solid" is not rigidly clear.

    tschüss

    EB
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