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

  • question_answer A cone, a hemisphere and a cylinder stand on equal bases and have the same height what is the ratio of their volumes?

    A)  \[2:1:3\]                       

    B)  \[2.5:1:3\]     

    C)  \[1:2:3\]   

    D)  \[1.5:2:3\]

    Correct Answer: C

    Solution :

    (c): As they stand on the same base so their radius is also same. Then; volume of cone \[=\frac{\pi {{r}^{2}}h}{3}\] Volume of hemisphere \[=\frac{2\pi {{r}^{3}}}{3}\];     Volume of cylinder \[=\pi {{r}^{2}}h\] Ratio \[=\frac{\pi {{r}^{2}}h}{3}:\frac{2\pi {{r}^{3}}}{3}:\pi {{r}^{2}}h\] \[\Rightarrow \]   \[\frac{h}{3}:\frac{2r}{3}:h\] \[\Rightarrow \]   \[h:2r:3h\]      Radius of a hemisphere = It?s height So,      \[h:2h:3h\Rightarrow 1:2:3\]        

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