10th Class Mathematics Solved Paper - Mathematics-2018

  • question_answer 21)
    A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 3. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the article.
    OR
    A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

    Answer:

    Given, Radius (r) of cylinder = Radius of hemisphere = 3.5 cm.
                    Total SA of article = CSA of cylinder \[+2\times \] CSA of hemisphere
                Height of cylinder, h = 10 cm
    TSA  \[=\text{ }2\pi rh+2\times 2\pi {{r}^{2}}\]
             \[=2\pi rh+4\pi {{r}^{2}}\]
             \[=2\pi r\text{ (}h+2r)\]
             \[=2\times \frac{22}{7}\times 3.5(10+2\times 3.5)\]
             \[=2\times 22\times 0.5\times (10+7)\]
             \[=2\times 11\times 17\]
             \[=374\,\,c{{m}^{2}}\]
    OR
    Base diameter of cone = 24 m.
    \[\therefore \] Radius \[r=12\text{ }m\]
    Height of cone, \[h=3.5\text{ }m\]
    Volume of rice in conical heap
                            \[=\frac{1}{3}\pi {{r}^{2}}h\]
                            \[=\frac{1}{3}\times \frac{22}{7}\times 12\times 12\times 3.5\]
                            \[=528\,{{m}^{3}}\]
    Now, slant height, \[l=\sqrt{{{h}^{2}}+{{r}^{2}}}\]
                                 \[=\sqrt{{{(3.5)}^{2}}+{{(12)}^{2}}}\]
                                 \[=\sqrt{12.25+144}\]
                                  \[=\sqrt{156.25}\]
                               \[=12.5\,m\]
    Canvas cloth required to just cover the heap =
    CSA of conical heap \[=\pi rl\]
                                   \[=\frac{22}{7}\times 12\times 12.5\]
                                   \[=\frac{3300}{7}{{m}^{2}}\]
                                   \[471.43\,\,{{m}^{2}}\].   


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