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

  • question_answer A vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the sphere is 14 cm and the total height of the vessel is 13 cm. find the capacity of the vessel. (Take \[\pi =22/7\])

    A)  \[321.33\text{ }c{{m}^{3}}\]              

    B)  \[1642.67\text{ }c{{m}^{3}}\]  

    C)  \[1232\text{ }c{{m}^{3}}\]                 

    D)  \[1632.33\text{ }c{{m}^{3}}\]

    Correct Answer: B

    Solution :

    (b): Height of the cylinder = 13 ? 7 = 6 cm Radius of the cylinder and the hemisphere = 7cm Volume of the vessel = volume of cylinder + volume of hemisphere \[\Rightarrow \]   \[\pi {{r}^{2}}h+\frac{4\pi {{r}^{3}}}{3\times 2}\] \[\Rightarrow \]   \[3.14\times {{(7)}^{2}}\times 6+\frac{4\times 3.14\times {{(7)}^{3}}}{3\times 2}\] \[\Rightarrow \]   \[1642.67\,\,c{{m}^{3}}\]            

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