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

  • question_answer A cylinder and a cone having equal diameter of their bases are placed in the form of a Minar, one over the other, with the cylinder placed at the bottom. If their curved surface areas of cylinder & cone are in the ratio of \[8:5\] respectively, find the ratio of their heights. Assume the height of the cylinder to be equal to the radius of the Minar. (Assume the Minar to be having same radius throughout).

    A)  \[1:4\]                          

    B)  \[3:4\]         

    C)  \[4:3\]    

    D)  \[2:3\]

    Correct Answer: C

    Solution :

    (c): As the cylinder and cone have equal diameters. So they have equal area. Let cone?s height be \[{{h}_{2}}\] and as per question, cylinder?s height be \[{{h}_{1}}\] \[\frac{2\pi r{{h}_{1}}}{\pi r\sqrt{h_{2}^{2}+{{r}^{2}}}}=\frac{8}{5}\] and put \[{{h}_{1}}=r\] The desired ratio is \[4:3\]                        

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