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

  • question_answer A spherical cannon ball, 28 cm in diameter, is melted and cast into a right circular conical mould the base of which is 35 cm in diameter. Find the height of the cone correct up to two places of decimals.

    A)  8.96 cm                       

    B)  35.84 cm   

    C)  5.97 cm          

    D)  17.92 cm

    Correct Answer: B

    Solution :

    (b): The volume in both the cases will be equal. Let the height of cone be = h \[4\times \frac{22}{7}\times {{(14)}^{3}}\times \frac{1}{3}=\frac{22}{7}\times {{\left( \frac{35}{2} \right)}^{2}}\times \frac{h}{3}\] \[\Rightarrow \]   \[4{{(14)}^{3}}=h{{\left( \frac{35}{2} \right)}^{2}}\] \[\Rightarrow \]   \[h=\frac{4\times 14\times 14\times 14\times 2\times 2}{35\times 35}\] \[=\]     \[h=35.84\,\,cm\] (Mind of a mathematician; Students should remember figures like \[{{11}^{2}}=121,\,\,\,{{11}^{3}}=1331;\] \[{{12}^{2}}=144,\,\,\,{{12}^{3}}=1728\]and these should be at the tip of their tongue.)  

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