While rummaging in his great aunt's attic, Bernard found a small figurine that he believed to be made out of silver. To test his guess, he looked up the denisty of silver in his chemistry book and found it to be 10.5 g/cm^3. He found that 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 silve, by how much did the water level in the glass rise?
V = (149g/10.5g) * 1cm^2 = 14.2 cm^3. =
Vol. of the figure.
V = pi*r^2 * h = 14.2 cm^3.
3.14*3^2 * h = 14.2.
h = 0.50 cm.
To find out by how much the water level in the glass rises when Bernard drops the figurine made of silver into it, we need to calculate the volume of the figurine.
The volume of an object can be calculated using the formula:
Volume = Mass / Density
In this case, the mass of the figurine is given as 149 g, and the density of silver is given as 10.5 g/cm^3. Therefore, we can calculate the volume as follows:
Volume = Mass / Density
Volume = 149 g / 10.5 g/cm^3
Volume ≈ 14.19 cm^3
Now that we have the volume of the figurine, we can determine the displacement of water when the figurine is dropped into the glass.
The displacement of water is equal to the volume of the figurine. Since the figurine was dropped into a cylindrical glass with a diameter of 6 cm, we can use the formula for the volume of a cylinder to determine the displacement.
The formula for the volume of a cylinder is:
Volume = π * r^2 * h
In this case, we know the diameter is 6 cm, so the radius (r) would be half of the diameter, which is 3 cm. The height (h) would be the amount the water level rises.
Volume = π * r^2 * h
14.19 cm^3 = π * (3 cm)^2 * h
To solve for h, we can rearrange the equation as follows:
h = 14.19 cm^3 / (π * (3 cm)^2)
h ≈ 0.53 cm
Therefore, the water level in the glass would rise by approximately 0.53 cm when Bernard drops the figurine made of pure silver into it.