Verified Answer :

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 = \(5.00 cm \times 4.00 cm \times 1.00 cm = 20.00 cm^3=20.00 mL\)

(\(1 cm^3= 1mL\))

Mass of an iron cube = m

\(Density=\frac{Mass}{Volume}\)

\(m =Density\times Volume =7.87 g/mL\times 20.00 mL=157.4 g\)

The mass of iron is 157.4 g.

mariejoepagaduan

The mass of the block of iron is 157 g.

FURTHER EXPLANATION

Density is the measure of the compactness of a material. It is the mass per given volume. This can be expressed mathematically as:

\(Density \ (\rho) \ = \frac{Mass \ (M)}{Volume \ (V)}\)  (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:

\(Mass \ (M) \ = Density (\rho) \ x \ Volume (V)\\M = \rho V\) (equation 2)

To calculate the volume,

\(Volume (V) \ = \frac{Mass \ (M)}{Density \ (\rho)}\\ V \ = \frac{M}{\rho}\) (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:

\(M = \rho V\\M = (7.87 \frac{g}{mL}) (20.0 mL)\\\boxed {M = 157.4 \ g}\)

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.

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Keywords: density, solid

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