College

[tex]2.5 \, m^3[/tex] of limestone has a mass of [tex]6025 \, kg[/tex].

a) Calculate the density of limestone in [tex]kg/m^3[/tex].

b) Find the mass of [tex]1.7 \, m^3[/tex] of limestone in [tex]kg[/tex].

Answer :

We are given that a volume of limestone of
[tex]$$2.5 \, \mathrm{m^3}$$[/tex]
has a mass of
[tex]$$6025 \, \mathrm{kg}.$$[/tex]

Step 1: Calculate the density

The density [tex]\( \rho \)[/tex] is given by the formula
[tex]$$
\rho = \frac{\text{mass}}{\text{volume}}.
$$[/tex]

Substitute the given values into the formula:
[tex]$$
\rho = \frac{6025 \, \mathrm{kg}}{2.5 \, \mathrm{m^3}} = 2410 \, \mathrm{kg/m^3}.
$$[/tex]

So, the density of the limestone is
[tex]$$2410 \, \mathrm{kg/m^3}.$$[/tex]

Step 2: Calculate the mass of [tex]\(1.7 \, \mathrm{m^3}\)[/tex] of limestone

To find the mass of a different volume of limestone, use the formula:
[tex]$$
\text{mass} = \rho \times \text{volume}.
$$[/tex]

Here, the volume is given as
[tex]$$1.7 \, \mathrm{m^3}$$[/tex]
and the density is
[tex]$$2410 \, \mathrm{kg/m^3}.$$[/tex]

Thus,
[tex]$$
\text{mass} = 2410 \, \mathrm{kg/m^3} \times 1.7 \, \mathrm{m^3} = 4097 \, \mathrm{kg}.
$$[/tex]

Final Answers:

a) The density of the limestone is
[tex]$$2410 \, \mathrm{kg/m^3}.$$[/tex]

b) The mass of [tex]\(1.7 \, \mathrm{m^3}\)[/tex] of limestone is
[tex]$$4097 \, \mathrm{kg}.$$[/tex]