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A solid cube has been cut …

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A solid cube has been cut into two cuboids of equal volumes. Find the ratio of TSA of one of the cuboids to that to the given cube.?

    • Posted by Gopesh Kawatra 5 years, 11 months ago

    CBSE > Class 09 > Mathematics
    • 2 answers

    Abhinav Soni 5 years, 11 months ago

    When this cube is cutted into two cuboids then, [As we know volume of cuboid is -> 2*(l*b+b*h+h*l)] Let one of those cuboid be x and another be y . Now, for the ratio of their TSA=> = volume of x cuboid/volume of y cuboid = 2*(l*b+b*h+h*l)/2*(l*b+b*h+h*l) Therefore now when we cancel out each of them so the results will be, = 1/1 = 1: 1

    0Thank You

    Yogita Ingle 5 years, 11 months ago

    The surface area of a cub is 6*(area of one face) = 6LW
    The volume of a cube is LWH
    acube = 6LW

    to make two equal cuboids, we cut the cube in half through its height - LW(.5H)
    The surface area of the cuboid is
    base + top + four sides
    LW + LW + 4(.5HL)
    2LW + 2LH
    acuboid = 2L(W+H)

    so the ratio of the cube to the cuboid is
    acube : acuboid
    6LW : 2L(W+H)
    now, the important part, since we started with a cube L = W = H, so we can simplify
    6LL : 2L(L+L)
    6L2 : 2L(2L)
    6L2 : 4 L2
    6:4
    3:2

    0Thank You

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