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Help me with math please!

Solid A is dilated using a scale factor of 2⁄5, resulting in Solid B. Solid B is also dilated using a scale factor of 2⁄5, resulting in Solid C. If the volume of Solid B is 72 〖km〗^3, what is the volume of Solid A and Solid C?

Sagot :

MrRoyalidn

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]

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