10th Class Mathematics Mensuration Question Bank Mensuration

  • question_answer
    A cuboid is such that its length is 2 times the width and the width is 2 times its height. The side of a square, whose area is equal to the total surface area of the cuboid, in terms of the height of the cuboid is

    A)  \[4h\]                  

    B)         \[6h\]

    C)  \[2\sqrt{7}h\]                                    

    D)  \[4\sqrt{7}h\]

    Correct Answer: C

    Solution :

     Let the height of the cuboid be h. Then, its width \[=2\,h\]and its length \[=4\,h\] \[\therefore \] Total surface area                 \[=2(4h\times 2h+4h\times h\times h\times 2h)\]                 \[=28\,{{h}^{2}}\]                                                            ?..(i) Let the side of the square be x. Then, its area \[={{x}^{2}}\]                                        ??(ii) From equations (i) and (ii)                 \[{{x}^{2}}=28\,{{h}^{2}}\] or            \[x=2\,\sqrt{7}\,h\]


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