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

  • question_answer A cylindrical container whose diameter is 12 cm and height is 15 cm, is filled with ice cream. The whole ice ? cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice ? cream cone. (radius of top of ice-cream cone = radius of hemisphere)

    A)  6 cm    

    B)  12 cm        

    C)  3 cm                           

    D)  18 cm

    Correct Answer: A

    Solution :

    (a): Volume of cylindrical container \[=\pi {{(6)}^{2}}15\] Volume of ice-cream cone = volume of the cone + volume of hemispherical top \[=\frac{1}{3}\pi {{r}^{2}}4r+\frac{2}{3}\pi {{r}^{2}}=2\pi {{r}^{3}}\] (Where ?r? is the radius of the cone). \[\therefore \]      \[10\times 2\pi {{r}^{3}}=\pi {{(6)}^{2}}15\] or \[{{r}^{3}}=27\] \[\Rightarrow \]   \[2r=2{{(27)}^{\frac{1}{3}}}=6\,\,cm\]                       

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