Question

Metal A has density of 3.2 g/cm3 and Metal B has density of 5.5 g/cm3. Metal C is made from
combining Metal A and Metal B in the ratio of 3:7. What is the density of Metal C if it has a mass
of 2500 g
full ans 3 marker question if antything else i wil report

Answer 1

Given : Metal A has density of 3.2 g/cm3

            Metal B has density of 5.5 g/cm3

             Metal C is is in the ratio of 3:7 and mass = 2500g

             Metal C is made of combining metal A and metal B

To Find : Density of Metal C

Solution:

Since we have been given the mass of metal C, and the ratio of metal A and metal B  we can therefore calculate the mass of metal A and metal B.  If the ratio of metal A to metal B is 3 :7, that means that $\[\frac{3}{{10}}\]$ of the mass of metal C comes from metal A and the remaining $\frac{7}{10}$  is metal B.

The mass of metal A can be calculated as follows:

                                                     $2500 g \times \dfrac{3}{10} =750 g$

The mass of metal B can be calculated as follows:

                                                     $2500 g \times \dfrac{7}{10}=1750 g$

We now know both the mass and density of both metals A and B

Since

                        $\[Density = \frac{{mass}}{{volume}}\]$

       Then

                        $\[Volume = \frac{{mass}}{{Density}}\]$

The volume of metal A can be calculated as follows

                  $750 g \div \, 3.2$ g/$\[c{m^3}\]$ = 234.375 $\[c{m^3}\]$

The volume of metal AA can be calculated as follows:

                   $1750 g \div \, 5.5 g/cm^3 = 318.18 3 =318.18 cm^3$

If metal A has a volume of $234.37cm^3$  and metal B has a volume of $318.18 cm^3$then their combined volume is the volume of metal C is :

$Volume of metal C = 234.375 + 318.18 = 552.55+318.18=552.55 cm^3$

We now know both the mass and volume of metal C , so we are now able to calculate its density :

           $Density of metal C = 2500 g \div \, 552.55 cm^3 = 4.5 3 g/cm^3 =4.5 g/cm^3$

Hence Density of metal C is $\[4.5g/c{m^3}\]$.