6th Class Mental Ability Mensuration Question Bank Mensuration

  • question_answer
    Find the lateral surface area of a cuboid whose length, breadth and height are in the ratio of 4 : 3 : 2 and volume of the cuboid is \[\mathbf{5184}\text{ }{{\mathbf{m}}^{\mathbf{3}}}.\]

    A) \[1408\text{ }{{m}^{2}}\]            

    B)        \[2008\text{ }{{m}^{2}}\]

    C) \[1016\text{ }{{m}^{2}}\]            

    D)       \[1008\text{ }{{m}^{2}}\]

    E) None of these

    Correct Answer: D

    Solution :

    Explanation Option [d] is correct. Let us consider the multiplier x. Hence, \[4x\times 3x\times 2x=5184\]\[\Rightarrow 24{{x}^{2}}=5184\] \[\Rightarrow {{x}^{3}}=\frac{5184}{24}\Rightarrow {{x}^{3}}=216\] \[\Rightarrow x=\sqrt[3]{216}=6.\] Length of the cuboid = 24 m/ width = 18 m and height = 12 m. Thus, the lateral surface area of the cuboid \[=2h\left( l+b \right)=2\times 12\left( 24+18 \right)=1008{{m}^{2}}.\]


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