a piece of iron measures 10.5cm by 5.25cm by 10.2mm and the density of theiron is 7.86g/cm cubed. what is the mass of the iron?

Convert 10.2mm to cm:

10.2mm*(10^-1cm/1mm)=10.2 x 10^-1 cm

Find the volume of the cube:

(10.5cm)*(5.25cm)*(10.2 x 10^-1 cm)=volume of cube

Density=mass/volume

Solve for mass:

Density*Volume=mass

7.86g/cm^3*Volume of cube=mass

To calculate the mass of the iron, we need to use the formula:

Mass = Density × Volume

First, let's calculate the volume of the iron. The iron is in the shape of a rectangular prism, so the volume can be found using the formula:

Volume = Length × Width × Height

Given:
Length = 10.5 cm
Width = 5.25 cm
Height = 10.2 mm

We need to make sure the dimensions are in the same unit before calculating the volume. Since the height is given in millimeters, let's convert it to centimeters:

Height = 10.2 mm = 1.02 cm (since 1 cm = 10 mm)

Now we can calculate the volume:

Volume = 10.5 cm × 5.25 cm × 1.02 cm

Next, let's calculate the mass by multiplying the volume by the density:

Mass = 7.86 g/cm³ × Volume

To find the final answer, we substitute the calculated value of the volume into the formula:

Mass = 7.86 g/cm³ × (10.5 cm × 5.25 cm × 1.02 cm)

Now we can solve this equation to find the mass of the iron.