Answer and Explanation
The volume of a cube is defined as:
[tex]V = s^3[/tex]
where [tex]s[/tex] is the cube's side length.
Plugging in the given side length of 5cm, we get:
[tex]V=(5\text{ cm})^3[/tex]
[tex]\boxed{V = 125\text{ cm}^3}[/tex]
Notice that [tex]s^3[/tex] can be broken down into:
[tex]s^3 = s^2 \cdot s[/tex]
which is in the form:
[tex]V = A_\text{base} \cdot h[/tex]
Since the side lengths of a cube are all the same, the area of the base simplifies to:
[tex]A = s^2[/tex],
and the height is just another [tex]s[/tex]. Hence, we get:
[tex]V = s^2 \cdot s = s^3[/tex]
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Next, we can find the surface area of the cube by multiplying its base area by 6, since there are 6 identical sides on a cube:
[tex]SA = 6A_\text{base}[/tex]
[tex]SA=6s^2[/tex]
[tex]SA = 6(5\text{ cm})^2[/tex]
[tex]SA = 6(25\text{ cm})[/tex]
[tex]\boxed{SA = 150\text{ cm}^2}[/tex]
