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

  • question_answer A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5 cm and its height is 32 cm, find the uniform thickness of the cylinder.

    A)  2 cm                           

    B)  3 cm         

    C)  1 cm    

    D)  3.5 cm

    Correct Answer: C

    Solution :

    (c): Let the internal radius of the cylinder = r Then the volume of sphere = volume of hollow cylinder \[\Rightarrow \]   \[\frac{4\pi {{.6}^{3}}}{3}=\pi h({{5}^{2}}-{{r}^{2}})\] \[\Rightarrow \]   \[\frac{864\pi }{3}=32\pi (25-{{r}^{2}})\] \[\Rightarrow \]   \[{{r}^{2}}=16=r=4\,cm\] So thickness of the cylinder = 5 ? 4 = 1 cm                      

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