question_answer

A right circular cylinder is circumscribed about a hemisphere so that they share the same base. The ratio of the volumes of cylinder and hemisphere is:

A)  4: 3                 

B)  3: 1

C)  3: 4                 

D)  3: 2

Correct Answer: D

Solution :

 Radius of the hemisphere = Rad. of the cylinder \[\therefore \] The cylinder circumscribes the hemisphere \[\Rightarrow \]Height of the cylinder = Rad. Of the hemisphere Volume of cylinder =         \[\pi {{r}^{2}}h=\pi {{r}^{2}}\times r=\pi {{r}^{3}}\] Volume of the hemisphere = \[\frac{2}{3}\pi {{r}^{3}}\] \[\therefore \]Required Ratio = \[\frac{\pi {{r}^{3}}}{\frac{2}{3}\pi {{r}^{3}}}=\]