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

  • question_answer A steel sphere of radius 4 cm is drawn into a wire of diameter 4 mm. Find the length of wire.

    A)  10665 mm       

    B)  42660 mm     

    C)  21333 mm  

    D)  14220 mm

    Correct Answer: C

    Solution :

    (c): The volume in both the cases would be the same. Therefore \[\frac{4\pi {{R}^{3}}}{3}=\pi {{r}^{2}}h\] \[\therefore \]      \[\frac{4\times 3.14\times {{(4\times 10)}^{3}}}{3}=3.14\times {{2}^{2}}\times h\] \[\Rightarrow \]   \[h=\frac{64000}{3}=21333.33\,mm\] (Note that R and r are different, R = radius of sphere = 4cm = 40mm, r = radius of wire\[\frac{4\,mm}{2}=2\,mm\]. Its better to immediately draw rough diagrams.)     


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