Answer:
The mass of iron is 157.4 g.
Explanation:
Density of iron = 7.87 g/mL
Length of the iron block = 5.00 cm
Breadth of the iron block = 4.00 cm
Height of the iron block = 1.00 cm
Volume of an iron cube = [tex] 5.00 cm \times 4.00 cm \times 1.00 cm = 20.00 cm^3=20.00 mL[/tex]
([tex]1 cm^3= 1mL[/tex])
Mass of an iron cube = m
[tex]Density=\frac{Mass}{Volume}[/tex]
[tex] m =Density\times Volume =7.87 g/mL\times 20.00 mL=157.4 g[/tex]
The mass of iron is 157.4 g.
The mass of the block of iron is 157 g.
Density is the measure of the compactness of a material. It is the mass per given volume. This can be expressed mathematically as:
[tex]Density \ (\rho) \ = \frac{Mass \ (M)}{Volume \ (V)}[/tex] (equation 1)
The equation can be rearranged to find the mass or volume of an object.
To get the mass, the equation below is used:
[tex]Mass \ (M) \ = Density (\rho) \ x \ Volume (V)\\M = \rho V[/tex] (equation 2)
To calculate the volume,
[tex]Volume (V) \ = \frac{Mass \ (M)}{Density \ (\rho)}\\ V \ = \frac{M}{\rho}[/tex] (equation 3)
To solve the problem, equation 2 will be used.
First, sort the given in the problem:
ρ = 7.87 g/mL
V = 5.00 cm x 4.00 cm x 1.00 cm
= 20.0 cm3
Note: 1 cm3 = 1 mL. Therefore,
V = 20.0 mL
M = ?
Next, plug in the values into equation 2:
[tex]M = \rho V\\M = (7.87 \frac{g}{mL}) (20.0 mL)\\\boxed {M = 157.4 \ g}[/tex]
Since the given have 3 significant figures, the final answer must be expressed with 3 significant figures, too. Therefore, the mass of the iron block is 157 g.
Keywords: density, solid
