10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-I

  • question_answer 21) Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (Use \[\pi =\frac{22}{7}\])

    Answer:

    Radius of the base of cylinder \[(r)=2.8\,m\]
    Radius of the base of the cone \[(r)=2.8\,m\]
    Height of the cylinder \[(h)=3.5\,m\]
    Height of the cone \[(H)=2.1\,m\].
    Slant height of conical part \[(l)=\sqrt{{{r}^{2}}+{{H}^{2}}}\]
                                        \[=\sqrt{{{(2.8)}^{2}}+{{(2.1)}^{2}}}\]
                                        \[=\sqrt{7.84+4.41}\]
                                        \[=\sqrt{12.25}\]
                                        \[=3.5\,m\]
    Area of canvas used to make tent
    = CSA of cylinder + CSA of cone
    \[=2\times \pi \times 2.8\times 3.5+\pi \times 2.8\times 3.5\]
    \[=61.6+30.8\]
    \[=92.4\text{ }{{m}^{2}}\]
    Cost of 1500 tents at Rs. 120 per sq. m
    \[=1500\times 120\times 92.4\]
    \[=Rs.\,\,16,632,000\]
    Share of each school to set up the tents
    \[=\frac{16632000}{50}\]
    \[=Rs.\,332,640\]
    Value ? Be kind and help others in need.


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