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

  • question_answer A hollow sphere of external and internal radius 6 cm and 4 cm respectively is melted into a cone of base diameter 8 cm. find the height of the cone.

    A)  4.75 cm                       

    B)  9.5 cm       

    C)  19 cm             

    D)  38 cm

    Correct Answer: D

    Solution :

    (d): The volume in both the cases would be the same. Let the height of the cone = h, its radius = 4 cm Hollow sphere:- Then, external radius = 6 cm Internal radius \[=4\,\,cm\] \[\Rightarrow \]   \[\frac{4\pi \left( {{6}^{3}}-{{4}^{3}} \right)}{3}=\frac{\pi {{.4}^{2}}.h}{4}\] \[\Rightarrow \]   \[h=\frac{{{6}^{3}}-{{4}^{3}}}{4}\] \[\Rightarrow \]   \[h=\frac{216-64}{4}=38\,cm\]

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