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    The areas of three adjacent faces of a solid cuboid are 66 cm², 108 cm² and 198 cm². what is the volume (in cm³) of the cuboid?
    Question

    The areas of three adjacent faces of a solid cuboid are 66 cm², 108 cm² and 198 cm². what is the volume (in cm³) of the cuboid?

    A.

    594

    B.

    1188

    C.

    1782

    D.

    891

    Correct option is B

    Given:

    The areas of three adjacent faces of a cuboid are:

    A1=66 cm2A_1 = 66 \, \text{cm}^2​​

    A2=108 cm2A_2 = 108 \, \text{cm}^2​​

    A3=198 cm2A_3 = 198 \, \text{cm}^2​​

    Formula Used:

    Volume of cuboid,V = (ab)(bc)(ca)\sqrt{(ab)(bc)(ca)}​​

    Where a, b, c are dimensions

    Solution:

    Let the dimensions of the cuboid be a, b, and c. So, the areas of the three faces are:

    A1=ab=66 cm2A_1 = ab = 66 \, \text{cm}^2​​

    A2=bc=108 cm2A_2 = bc = 108 \, \text{cm}^2​​

    A3=ca=198 cm2A_3 = ca = 198 \, \text{cm}^2​​

    Now,

    V2=(66)(108)(198)V^2 = (66)(108)(198)​​

    V2=1411334V^2 = 1411334​​

    V = 1411334=1188 cm3\sqrt{1411334} = 1188 \, \text{cm}^3​​

    The volume of the cuboid is 1188 cm³.

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