10th Class Mathematics Solved Paper - Mathematics-2018

  • question_answer
    The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
    (i) The area of the metal sheet used to make the bucket.
    (ii) Why we should avoid the bucket made by ordinary plastic? [Use \[\pi =3.14\]]

    Answer:

    Given, Height of frustum, h = 24 cm.
    Diameter of lower end = 10 cm.
    \[\therefore \]      Radius of lower end, r = 5 cm.
    Diameter of upper end = 30 cm.
    \[\therefore \]      Radius of upper end, R = 15 cm.
    Slant height,       \[l=\sqrt{{{h}^{2}}+{{(R-r)}^{2}}}\]
                             \[=\sqrt{{{(24)}^{2}}+{{(15-5)}^{2}}}\]
                            \[=\sqrt{576+100}\]
                            \[=\sqrt{676}\]
                            \[=26\,cm\]
    (i) Area of metal sheet used to make the bucket
    = CSA of frustum + Area of base
    \[=\pi l(R+r)+\pi {{r}^{2}}\]
    \[=\pi [26(15+5)+{{(5)}^{2}}]\]
    \[=3.14(26\times 20+25)\]
    \[=3.14(520+25)\]
    \[=3.14\times 545\]
    \[=1711.3\,\,c{{m}^{2}}\]
    (ii) We should avoid the bucket made by ordinary plastic because plastic is harmful to the environment and to protect the environment its use should be avoided.


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