CLAT Sample Paper CLAT Sample Paper-8

  • question_answer
    Sum of the length, width and depth of a cuboid is 5 and its diagonal is d. Its surface area is

    A)  \[{{S}^{2}}\]                         

    B)  \[{{d}^{2}}\]             

    C)  \[{{S}^{2}}-{{d}^{2}}\]      

    D)         \[{{S}^{2}}+{{d}^{2}}\]

    Correct Answer: C

    Solution :

    Given that, \[l+b+h=S\]                         ...(i) and      \[\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}=d\]                      ...(ii) So,         \[{{l}^{2}}+{{b}^{2}}+{{h}^{2}}={{d}^{2}}\] \[\therefore \]      \[{{(l+b+h)}^{2}}={{S}^{2}}\] \[\Rightarrow \]   \[{{l}^{2}}+{{b}^{2}}+{{h}^{2}}+2\,(lb+bh+hl)={{S}^{2}}\] \[\Rightarrow \]   \[{{d}^{2}}+2\,(lb+bh+hl)={{S}^{2}}\] From Eq. (ii), \[2(lb+bh+hl)=({{S}^{2}}-{{d}^{2}})\] \[\therefore \]      Surface area \[=({{S}^{2}}-{{d}^{2}})\]

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