Question

A standard 1 kilogram weight is a cylinder 46.0 mm in height and 50.5 mm in diameter. What is the density of the material?

Answer 1

To find the density of the material, divide its mass by its volume. In this case, the density of the 1 kilogram weight is 27398.28 kg/m^3.

Step-by-step explanation:

The density of a material is determined by dividing its mass by its volume. In this case, we have a 1 kilogram weight with a height of 46.0 mm and a diameter of 50.5 mm. To find the volume of the weight, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. The radius is half the diameter, so r = 25.25 mm. Converting all measurements to meters, we have r = 0.02525 m and h = 0.046 m. Plugging in these values, we get V = π(0.02525^2)(0.046) = 3.6543 x 10^-5 m^3.

Now, we can calculate the density by dividing the mass of the weight (1 kg) by its volume: density = mass / volume = 1 kg / 3.6543 x 10^-5 m^3 = 27398.28 kg/m^3.

Answer 2

The density of the material is 10.9 g/cm³

Step-by-step explanation:

The formula of density (D) is given by:

`D=(mass)/(volume)`

You have to calculate the volumen of the cylinder, which is given by:

V = π r² h

where r is the radius and h is the height.

The formula can be written in therms of the diameter (d), using the fact that half the diameter is the radius:

V=π
`((d)/(2)) ^(2)`h

Calculating the volume:

V = π
`((50.5)/(2)) ^(2) (46.0)`

V = 92136.2 mm³

The volume in cm³ is: 92.1 cm³ (because 1000mm³=1cm³) and the mass in grams is: 1000g (because 1kg=1000g)

Calculating the density:

`D=(1000(g))/(92.1(cm^(3)) ) = 10.9 g/cm^(3)`