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]
[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]
