10th Class Mathematics Surface Areas and Volumes Question Bank Surface Area and Volume (Mensuration)

  • question_answer A conical tent is to accommodate 10 persons. Each person must have \[6\text{ }{{m}^{2}}\] space to sit and \[30\,\,{{m}^{3}}\] of air to breath. What will be the height of the cone?

    A)  37.5 m                        

    B)  150 m        

    C)  75 m               

    D)  None of these

    Correct Answer: D

    Solution :

    (d): Area of base \[=6\times 10=60\,\,{{m}^{2}}\] Volume of tent \[=30\times 10=300\,\,{{m}^{3}}\] Let the radius be = r, height = h, slant height = l \[\therefore \] \[\pi {{r}^{2}}=60\Rightarrow r=\sqrt{\frac{60}{\pi }}\] Also, \[300=\frac{\pi {{r}^{2}}h}{3}\] \[\Rightarrow \] \[900=\pi .\frac{60}{\pi }.h\] \[\Rightarrow \]\[h=15\,\,m\]

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