A) 2.3 cm
B) 5.1 cm
C) 1.5cm
D) 3.2cm
Correct Answer: A
Solution :
Let the initial depth of water in the can be \[x\,cm\] Then, volume of initial water column \[=\pi {{r}^{2}}h=\pi {{(3.5)}^{2}}\times c{{m}^{3}}\] Volume of the sphere \[=\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi {{(3.5)}^{2}}x\,c{{m}^{3}}\] Now, volume of initial water column + Volume of the sphere = Volume of the cylinder up to the height of water level \[\therefore \]\[\pi \times {{(3.5)}^{2}}\times x\,c{{m}^{3}}+\frac{4}{3}\pi {{(3.5)}^{3}}c{{m}^{3}}\] \[=\pi {{\left( \frac{7}{2} \right)}^{2}}7\,c{{m}^{3}}\] \[\Rightarrow \]\[x+\frac{4}{3}\times 3.5=7\]\[\Rightarrow \]\[x+\frac{14}{3}=7\] \[\Rightarrow \]\[x=7-\frac{14}{3}=\frac{7}{3}\] \[\therefore \]The depth of water in the can before the sphere was put into it =2.3 cmYou need to login to perform this action.
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