| Assume that a drop of water is spherical and its diameter is one-tenth of 1 cm. A conical glass has a height equal to the diameter of its rim. If 32000 drops of water fill the glass completely, then the height of the glass (in cm) is |
A) 1
B) 8
C) 3
D) 4
Correct Answer: B
Solution :
| Let the radius of rim of the glass be r, |
| Height of glass = 2r |
| According to the question, |
| \[32000\times \frac{4}{3}\pi \times \frac{1}{10}\times \frac{1}{10}\times \frac{1}{10}=\frac{1}{3}\pi \times {{r}^{2}}\times 2r\] |
| \[\Rightarrow \] \[\frac{32000\times 4}{1000}=2{{r}^{3}}\] |
| \[\Rightarrow \] \[{{r}^{3}}=64\]\[\Rightarrow \]\[r=4\] |
| \[\therefore \] Height of glass = 2r = 8 cm |
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