10th Class Mathematics Solved Paper - Mathematics 2017 Outside Delhi Set-III

  • question_answer 2) A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

    Answer:

    Given, radius of base \[r=3.5\text{ }cm\]
    Total height of toy \[=15.5\text{ }cm\]
    Height of cone \['h'=15.5-3.5\]
      \[=12cm\]       
    Slant height \['l'=\sqrt{{{h}^{2}}+{{r}^{2}}}\]
                         \[=\sqrt{{{12}^{2}}+{{3.5}^{2}}}\]
                         \[=\sqrt{144+12.25}\]
                         \[=\sqrt{156.25}\]
                         \[=12.5\,\,cm\]
    Total S.A. of toy = CSA of cone + CSA of hemisphere
             \[=\pi rl+2\pi {{r}^{2}}\]
             \[=\pi r\,[l+2r]\]
             \[=\frac{22}{7}\times 3.5[12.5+2\times 3.5]\]
             \[=22\times 0.5[12.5+7]\]
             \[=11\times 19.5\]
             \[=214.5\,\,c{{m}^{2}}\]


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