what is the mass density of mercury is 13.6g/cm^3. A cylinder of mercury has a diameter of 1 cm and a height of 76cm. what would the height of the cylinder of the water having a diameter of 1 cm and a mass equal to the mass of the mercury cylinder?
The mass of the mercury in the cylinder can be calculated by multiplying density x volume. Volume of a cylinder with radius (r) and height (h) is (πr^2)h. Remember radius is 1/2 diameter. So, mass of mercury = (13.6 g/cm^3) x ((π(0.5cm)^2)76cm = 59.67 g.
The height of a 1 cm diameter cylinder holding 59.67 g water can be found using the same equation for volume of a cylinder, assuming the density of water is 1g/cm^3, volume = (πr^2)h. 59.67g water = 59.67cm^3 = (π(0.5^2))h. Solving for h shows height is 76 cm.
My apologies... I neglected to multiply out the density of mercury, which yields 811.79g mercury. Solving for h then shows that water cylinder is 1033.6 cm.
(13.6 g/cm^3)((π(0.5cm)^2)76cm) = (π(0.5^2))h
To solve this problem, we need to understand that mass density is defined as mass divided by volume.
Given that the mass density of mercury is 13.6 g/cm^3, we can calculate the mass of the mercury cylinder by finding its volume and then multiplying it by the mass density.
The volume of a cylinder can be calculated using the formula:
Volume = π * radius^2 * height
Since the diameter of the cylinder is given as 1 cm, the radius will be half of that, which is 0.5 cm.
Also, the height of the mercury cylinder is given as 76 cm.
Let's calculate the volume of the mercury cylinder:
Volume = π * (0.5 cm)^2 * 76 cm
Volume = 3.14 * (0.25 cm^2) * 76 cm
Volume = 59.52 cm^3
Now, we can calculate the mass of the mercury cylinder:
Mass = Mass density * Volume
Mass = 13.6 g/cm^3 * 59.52 cm^3
Mass = 810.432 g
Since water has a mass density of 1 g/cm^3, we can set up an equation to find the height of the water cylinder:
Mass of water cylinder = Mass of mercury cylinder
1 g/cm^3 * Volume of water cylinder = 810.432 g
The volume of the water cylinder can be calculated using its height and diameter. Since the diameter is given as 1 cm, the radius will be 0.5 cm.
Let's plug in the values and solve for the height of the water cylinder:
1 g/cm^3 * π * (0.5 cm)^2 * Height of water cylinder = 810.432 g
Simplifying the equation:
(0.25 π cm^3) * Height of water cylinder = 810.432 g
Height of water cylinder = 810.432 g / (0.25 π cm^3)
Height of water cylinder ≈ 1030.4 cm
Therefore, the height of the cylinder of water with a diameter of 1 cm and a mass equal to the mass of the mercury cylinder would be approximately 1030.4 cm.
To find the height of the water cylinder, we can use the equation:
V = A * h,
where V is the volume, A is the area of the base, and h is the height.
First, let's find the volume of the mercury cylinder. The formula for the volume of a cylinder is:
V = π * r^2 * h,
where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.
Given that the diameter of the mercury cylinder is 1 cm, the radius can be calculated by dividing the diameter by 2:
r = 1 cm / 2 = 0.5 cm.
Now, let's calculate the volume of the mercury cylinder:
V_mercury = π * (0.5 cm)^2 * 76 cm.
Next, we need to find the mass of the mercury cylinder using the mass density:
m_mercury = density * V_mercury.
Substituting the given density of mercury (13.6 g/cm^3) and the volume we calculated above:
m_mercury = 13.6 g/cm^3 * V_mercury.
Now, we need to find the mass of the water cylinder since it has the same mass as the mercury cylinder. The density of water is 1 g/cm^3.
m_water = m_mercury = 13.6 g/cm^3 * V_water.
We can now rearrange the formula to solve for V_water:
V_water = m_water / 13.6 g/cm^3.
Finally, substitute the volume of the water into the equation for the volume of a cylinder to find the height:
V_water = π * (0.5 cm)^2 * h_water.
Solve for h_water:
h_water = V_water / (π * (0.5 cm)^2).
By substituting the calculated value of V_water, we can find the height of the water cylinder.