| A cylindrical vessel of diameter 12 cm is partly filled with water. A spherical ball is dropped in it and the water level raised by 1 cm. The diameter of the ball m |
A) 6 cm
B) \[6\sqrt{3}\,\text{cm}\]
C) 3 cm
D) 9 cm
Correct Answer: A
Solution :
| Volume of spherical ball \[=\frac{4}{3}\pi {{r}^{3}}\] |
| and volume of raised water \[=\pi {{\left( \frac{12}{2} \right)}^{2}}\times 1=36\pi \] |
| Volume of spherical ball = Volume of raised water |
| \[\Rightarrow \] \[\frac{4}{3}\pi {{r}^{3}}=36\pi \] |
| \[\Rightarrow \] \[4{{r}^{3}}=3\times 36\]\[\Rightarrow \]\[{{r}^{3}}=\frac{3\times 36}{4}\] |
| \[\Rightarrow \] \[{{r}^{3}}=3\times 9=27\] |
| \[\Rightarrow \] \[{{r}^{3}}={{(3)}^{3}}\]\[\Rightarrow \]\[r=3\] |
| So, radius of spherical ball = 3 cm |
| Now, diameter of spherical ball \[=2\times \] Radius |
| \[=2\times 3=6\,cm\] |
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