Answer:
The volume of the larger cube is [tex]V=1,331\ cm^3[/tex]
Step-by-step explanation:
Let
x ---> the length of the smaller cube
y ---> the length of the larger cube
we know that
the volume of a cube is equal to
[tex]V=b^3[/tex]
where
b is the length side of the cube
we have
[tex]x=y-5[/tex] ----> equation A
The volume of the smaller cube is 216 cm^3
so
substitute in the formula of volume
[tex]216=x^3[/tex]
solve for x
[tex]x=\sqrt[3]{216}\ cm[/tex]
[tex]x=6\ cm[/tex]
Find the value of y
[tex]x=y-5[/tex]
[tex]6=y-5[/tex]
[tex]y=6+5=11\ cm[/tex]
Find the volume of the larger cube
[tex]V=y^3[/tex]
substitute the value of y
[tex]V=11^3[/tex]
[tex]V=1,331\ cm^3[/tex]
