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

  • question_answer A hemispherical bowl is filled with hot water to the brim. The contents of the bowl are transferred into a cylindrical vessel whose radius id 50% more than its height. If diameter of the bowl is the same as that of the vessel and the volume of the hot water in the cylindrical vessel is x% of the volume of the cylindrical vessel then x =?

    A)  90                               

    B)  100       

    C)  105                             

    D)  110

    Correct Answer: B

    Solution :

    (b): If radius of the hemispherical bowl is ?r? then it's volume would be \[\frac{2}{3}\pi {{r}^{3}}\] Radius of cylinder = r and height = 2r/3 Volume of cylinder \[=\pi {{r}^{2}}.\frac{2}{3}r=\frac{2}{3}\pi {{r}^{3}}\] It means that the volume of the hot water in the cylindrical vessel is 100 % of the cylindrical vessel, Therefore x = 100  

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