A) 1 ; 16 |
B) 1 : 12 |
C) 1 : 8 |
D) 1 : 4 |
D) 1 : 4 |
Volume of cylinder = \( \Large \pi r_{1}^{2}h \)
Volume of sphere = \( \Large \frac{4}{3} \pi r_{2}^{3} \)
Number of spheres = 48
Therefore, \( \Large \frac{Volume \ of \ cylinder}{Volume \ of \ sphere} = \frac{ \pi r_{1}^{2}h}{\frac{4}{3} \pi r_{2}^{3}} \)
=> \( \Large \frac{ \pi r_{1}^{2}h}{\frac{4}{3} \pi r_{2}^{3}} = 48 \)
=> \( \Large \left(Because, r_{1} = h\right) \)
=> \( \Large \frac{3}{4} \left(\frac{r_{1}}{r_{2}}\right)^{3} = 48 \)
=> \( \Large \left(\frac{r_{1}}{r_{2}}\right)^{3} = \frac{48 \times 4}{3} \)
\( \Large \left(\frac{r_{1}}{r_{2}}\right)^{3} = 64 \)
=> \( \Large \frac{r_{1}}{r_{2}} = 4 \)
=> \( \Large \frac{r_{1}}{r_{2}} = \frac{1}{4} \)