While rummaging, Bernard found a figurine that he believed to be made out of silver. To test his guess, he looked up the density of silver and found it to be 10.5g/cm^3. The figure had a mass of 149 g. To determine its volume, he dropped it into a cylindrical glass of water. If the diameter of the glass was 6 cm and the figurine was pure silver, by how much did the water level in the glass rise?
Archimedes would have been proud of you ...
The figure would replace (rise of water) its own volume of water.
volume of figurine = 149 g/(10.5 g/cm^3)
= 14.190476... cm^3
volume of water in cylinder = πr^2 h
= π(3^2)h
9πh = 14.19047..
h = 14.19047../(9π) = appr .502 cm
about 1/2 a cm
That you so much. Archimedes is probably turning over in his grave!!
To determine by how much the water level in the glass rose, we need to calculate the volume of the figurine and then compare it to the volume of water displaced by the figurine.
To find the volume of the figurine, we can use the formula:
Volume = Mass / Density
Given that the mass of the figurine is 149 g and the density of silver is 10.5 g/cm^3, we can substitute these values into the formula:
Volume = 149 g / 10.5 g/cm^3
Simplifying, we get:
Volume = 14.19 cm^3
Now let's calculate the volume of water displaced by the figurine.
The figure was dropped into a cylindrical glass of water. To find the volume of water displaced, we need to calculate the volume of a cylinder.
The formula to find the volume of a cylinder is:
Volume = π * r^2 * h
where π is a constant approximately equal to 3.1415, r is the radius of the cylinder, and h is its height.
Given that the diameter of the glass is 6 cm, the radius can be calculated by dividing the diameter by 2:
Radius = 6 cm / 2 = 3 cm
We don't have the height of the water level, but the problem states that the water level rose by a certain amount. So let's assume that the figurine was fully submerged, and the water level rose precisely up to the top of the figurine.
In this case, the height of the water level would be the same as the height of the figurine.
Now, we have all the necessary values to calculate the volume of water displaced:
Volume of water displaced = π * (3 cm)^2 * h
Now, let's focus on finding the height (h) of the water level.
The volume of water displaced by the figurine should be equal to the volume of the figurine:
14.19 cm^3 = π * (3 cm)^2 * h
Now we can solve for h:
h = 14.19 cm^3 / (π * 9 cm^2)
Simplifying, we get:
h ≈ 0.52 cm
So, the water level in the glass rose by approximately 0.52 cm due to the presence of the silver figurine.