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ACION



A student claims that if you dilate the net for a cube using a scale factor of 2, the surface



area of the resulting cube is multiplied by 4 and the volume is multiplied by 8. Does this



claim make sense?



(select)



make sense.

Respuesta :

Answer:Yes

Step-by-step explanation:

Given

Suppose side length of cube is a

If we dilate the cube using a scale factor of 2

Side length becomes 2a

and the surface area becomes [tex]=6(\text{side length})^2[/tex]

Surface area[tex]=6(2a)^2[/tex]

Surface area[tex]=4\times 6(a)^2[/tex]

Thus surface area multiplied by a factor of 4

Now for volume

[tex]V=(\text{side length })^3[/tex]

[tex]V=(2a)^3[/tex]

[tex]V=8(a^3)[/tex]

Therefore volume is multiplied by a factor of 8

Therefore the above statements make sense

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