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SSC Quantitative Aptitude Mensuration Question Bank Mensuration-II (I)

  • question_answer
    The volume of a conical tent is 1232 cu m and the area of its base is 154 sq m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width.\[\left( \text{take}\,\pi =\frac{22}{7} \right)\]

    A) 270 m

    B) 272 m

    C) 276 m

    D) 275 m

    Correct Answer: D

    Solution :

    [d] Let radius of base of conical tent be r m and it's height be h m. Then,\[\pi {{r}^{2}}=154\] \[\Rightarrow \]   \[{{r}^{2}}=154\times \frac{7}{22}=49\] \[\Rightarrow \]   \[r=7\,m\]and \[\frac{1}{3}\pi {{r}^{2}}h=1232\] \[\Rightarrow \]   \[h=1232\times 3\frac{7}{22}\times \frac{1}{7\times 7}=24\,m\] Now,     \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}\] \[=\sqrt{49+576}=\sqrt{625}=25\,m\] \[\therefore \]Area of required canvas = Curved surface of tent \[=\pi rl=\frac{22}{7}\times 7\times 25\] \[=550\,sq\,cm\] \[\therefore \]Length of canvas \[=\frac{550}{2}=275\,m\].


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