Answer:
512 in³
Step-by-step explanation:
the volume (V) of a cube is calculated as
V = s³ ( s is the side length )
given V = 64 in³ , then
s³ = 64 ( take cube root of both sides )
s = [tex]\sqrt[3]{64}[/tex] = 4
doubling s gives s = 2 × 4 = 8 , then
volume of new cube = 8³ = 512 in³
A cube has a volume of 64 inches³.If you double the length of each edge, what will be the volume of the new cube?
[tex] \small \underline {\underline{\rm{ First \: we \: will \: calculate \: the \: length \: of \: the \: cube \: using \: the \: volume.}}}[/tex]
We know,
[tex] \bull \: \small\boxed{ \rm{ Volume_{(cube)} = side³ }}[/tex]
So,
[tex] \bull \: \small \boxed{\rm{ side = \sqrt[3]{volume} }}[/tex]
Substituting the values we get
[tex] \small\rm{side = \sqrt[3]{64} = 4 \: inches} [/tex]
[tex] \small{ \underline{ \underline{\rm{ Now \: we \: will \: calculate \: the \: new \: volume}}}}[/tex]
It is given that the length is double
Double of 4 inches = 4 × 2 = 8 inches.
[tex] \small\sf{ New \: volume = 8³ = 8 × 8 × 8 = 512 \: inches³}[/tex]
