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Answer:
[tex]Solid\ A= 180km^3[/tex]
[tex]Solid\ C = 28.8km^3[/tex]
Step-by-step explanation:
Given
[tex]k_1 = \frac{2}{5}[/tex] from A to B
[tex]k_2 = \frac{2}{5}[/tex] from B to C
[tex]Solid\ B = 72km^3[/tex]
Required
Find the volumes of solids A and C
The expression that gives solid B from A is:
[tex]Solid\ A * k_1 = Solid\ B[/tex]
This gives:
[tex]Solid\ A * \frac{2}{5}= 72km^3[/tex]
Make A the subject
[tex]Solid\ A= 72km^3 * \frac{5}{2}[/tex]
[tex]Solid\ A= 36km^3 * 5[/tex]
[tex]Solid\ A= 180km^3[/tex]
Similarly:
The expression that gives solid C from B is:
[tex]Solid\ B * k_2 = Solid\ C[/tex]
This gives:
[tex]72km^3 * \frac{2}{5} = Solid\ C[/tex]
[tex]\frac{144km^3 }{5} = Solid\ C[/tex]
[tex]28.8km^3 = Solid\ C[/tex]
[tex]Solid\ C = 28.8km^3[/tex]