| A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 5 cm and height 6 cm. How much bottles are necessary to empty the bowl? |
A) 40
B) 20
C) 30
D) 60
Correct Answer: D
Solution :
| Radius of hemispherical bowl \[=15\,\,\,cm\] |
| Capacity of bowl with \[r=15=\frac{2\pi \,\,{{r}^{3}}}{3}\] |
| \[=\frac{2}{3}\times \pi \times {{(15)}^{3}}=2250\pi \,\,c{{m}^{3}}\] |
| Radius of cylindrical bottle \[=5/2\,\,cm\] |
| Height of cylindrical bottle \[=6\,\,cm\] |
| Volume of cylindrical bottle \[=\pi {{r}^{2}}h\] |
| \[=\pi \times {{(5/2)}^{2}}\times 6=\frac{75\pi }{2}c{{m}^{3}}\] |
| \[\therefore \]Number of bottles required |
| \[=\frac{\text{Capacity}\,\,\text{of}\,\,\text{bowl}}{\text{Volume}\,\,\text{of}\,\,\,\text{cylidrical}\,\,\text{bottle}}\] |
| \[=\frac{2250\pi }{\frac{75\pi }{2}}=\frac{2250\times 2}{75}=60\] |
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