6th Class Mathematics Mensuration Question Bank Mensuration (Perimeter & Area, Review of Earlier Concepts)

  • question_answer If the ratio of circumference of two circle is \[4:9,\] what is the ratio of their areas?

    A) \[9:4\]                          

    B)  \[16:81\]

    C) \[4:9\]              

    D)  \[2:3\]

    Correct Answer: B

    Solution :

    \[\left. \begin{align}   & Circle-1:\,\,{{C}_{1}}=2\pi {{r}_{1}} \\  & Circle-2:\,\,{{C}_{2}}=2\pi {{r}_{2}} \\ \end{align} \right\}\]Now, \[\frac{2\pi {{r}_{1}}}{2\pi {{r}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{4}{9};\] Area ratio \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{\pi {{r}_{1}}^{2}}{\pi {{r}_{2}}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\] \[={{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{81}\]

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