Answer:
[tex]V=2197\ cm^3[/tex]
Step-by-step explanation:
Surface Area and Volume of a Cube
Given a cube of side length a, the surface area is:
[tex]A = 6a^2[/tex]
The volume is calculated as:
[tex]V=a^3[/tex]
It's given the surface area of a cube:
[tex]A=1014\ cm^2[/tex]
We can find the side length a by solving for a:
[tex]\displaystyle a=\sqrt{\frac{A}{6}}[/tex]
[tex]\displaystyle a=\sqrt{\frac{1014}{6}}[/tex]
[tex]\displaystyle a=\sqrt{169}[/tex]
a = 13 cm
Now compute the volume:
[tex]V=13^3[/tex]
[tex]\boxed{V=2197\ cm^3}[/tex]
Answer: a) 2197 cm^3
