Mercury has a density of 13.6 g/cm3. What is the mass of a sample of mercury in a cylindrically shaped vial of radius 8 cm and height 10 cm?
The mass of the sample of mercury is 11,648 g.
To calculate this, first calculate the volume of the vial:
Volume = πr2h
Volume = 3.14 x (8 cm)2 x (10 cm)
Volume = 2,048 cm3
Then, calculate the mass of the sample of mercury:
Mass = Density x Volume
Mass = 13.6 g/cm3 x 2,048 cm3
Mass = 11,648 g
To find the mass of a sample of mercury in a cylindrically shaped vial, we need to multiply the volume of the cylinder by the density of mercury.
The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h
where π is a constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.
In this case, the radius (r) of the vial is given as 8 cm and the height (h) is given as 10 cm.
Therefore, the volume of the cylinder is:
Volume = π * (8 cm)^2 * 10 cm
= π * 64 cm^2 * 10 cm
= 640π cm^3
Now, we can use this volume along with the density of mercury to find the mass of the sample.
Mass = Volume * Density
= 640π cm^3 * 13.6 g/cm^3
To get the exact numerical value, we can use an approximation for the value of π, such as 3.14159.
Mass ≈ 640 * 3.14159 * 13.6 g
≈ 278250.1630464 g
Rounding to an appropriate number of significant figures, the mass of the sample of mercury in the cylindrically shaped vial is approximately 278,250 g.
To find the mass of the sample of mercury, we can use the equation:
Mass = Density × Volume
First, we need to calculate the volume of the sample.
The volume of a cylinder can be calculated using the formula:
Volume = π × radius^2 × height
Given that the radius of the vial is 8 cm and the height is 10 cm, we can substitute these values into the formula:
Volume = π × (8 cm)^2 × 10 cm
Volume = 3.14 × 64 cm^2 × 10 cm
Volume = 2009.6 cm^3
Now, we can calculate the mass using the density:
Mass = 13.6 g/cm^3 × 2009.6 cm^3
Mass = 27354.56 g
Therefore, the mass of the sample of mercury in the cylindrical vial is 27354.56 grams.