10th Class Mathematics Surface Areas and Volumes Question Bank Surface Area and Volume (Mensuration)

  • question_answer If the curved surface area of first cone is thrice that of another cone whereas slant height of the second cone is thrice that of the first, find the ratio of the area of their base.

    A)  \[81:1\] 

    B)  \[9:1\]           

    C)  \[3:1\]                          

    D)  \[27:1\]

    Correct Answer: A

    Solution :

    (a): Let the slant height of 1st cone = L Then the slant height of 2nd cone = 3L Let the radius of 1st cone \[={{r}_{1}}\] And let the radius of 2nd cone \[={{r}_{2}}\] Then,    \[\pi {{r}_{1}}L=3\times \pi {{r}_{2}}\times 3L\] \[\Rightarrow \]   \[\pi {{r}_{1}}L=9\pi {{r}_{2}}L\] \[\Rightarrow \]   \[{{r}_{1}}=9{{r}_{2}}\] Ratio of area of the base \[\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}\] \[\Rightarrow \]   \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}={{\left( \frac{9}{1} \right)}^{2}}\] \[\Rightarrow \]   \[81:1\]                         

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