Railways Sample Paper RRB (Group D) Sample Test Paper-12

  • question_answer
    If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is

    A)  \[351\,\,c{{m}^{2}}\]

    B)  \[256\,\,c{{m}^{2}}\]

    C)  \[265\,\,c{{m}^{2}}\] 

    D)  \[315\,\,c{{m}^{2}}\]

    Correct Answer: A

    Solution :

    [a] Let length=l, breadth=b, height=h. L+b+h=24 (given)         ... (i) Diagonal of parallellopiped=15 cm \[\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}=15\,\,or\,\,{{l}^{2}}+{{b}^{2}}+{{h}^{2}}=225\] Squaring eqn. (i) on both sides \[{{l}^{2}}+{{b}^{2}}+{{h}^{2}}+2lb+2bh+2hl=576\] \[2\,\,(lb+bh+hl)=576-\,225=351\] \[[\therefore \]Surface area of parallellopiped \[=2\,\,(lb+bh+hl)]\]

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