Question

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?

Answer 1

`Solid\ A= 180km^3`

`Solid\ C = 28.8km^3`

Explanation:

Given

`k_1 = (2)/(5)` from A to B

`k_2 = (2)/(5)` from B to C

`Solid\ B = 72km^3`

Required

Find the volumes of solids A and C

The expression that gives solid B from A is:

`Solid\ A * k_1 = Solid\ B`

This gives:

`Solid\ A * (2)/(5)= 72km^3`

Make A the subject

`Solid\ A= 72km^3 * (5)/(2)`

`Solid\ A= 36km^3 * 5`

`Solid\ A= 180km^3`

Similarly:

The expression that gives solid C from B is:

`Solid\ B * k_2 = Solid\ C`

This gives:

`72km^3 * (2)/(5) = Solid\ C`

`(144km^3 )/(5) = Solid\ C`

`28.8km^3 = Solid\ C`

`Solid\ C = 28.8km^3`