Answer:
[tex]\huge\boxed{1000 \ \text{cm}^3}[/tex]
Step-by-step explanation:
There are two ways we can solve this equation.
A) Using the formula provided
The formula provided states that the volume of a cube based on the area of one of it's faces will be [tex]a^{\frac{3}{2}}[/tex], a the area of one face. Since we know the area of one face, we can substitute that inside the equation.
[tex]100^{\frac{3}{2}}[/tex]
It's important to note that when we have a number to a fraction power, it's the same as taking the denominator root of the base to the numerator power.
So - [tex]100^{\frac{3}{2}}[/tex] becomes [tex]\sqrt{100^3}[/tex]
- [tex]\sqrt{1000000}=1000[/tex]
Therefore, the volume of this cube will be [tex]1000 \ \text{cm}^3[/tex]
B) Using prior knowledge about cubes
We can additionally use prior knowledge to find the volume of this cube.
We know that the area of a square will be [tex]s^2[/tex], where s is the length of a side. We also know the formula to find the volume of a cube from it's side length is [tex]s^3[/tex].
Since we know that one face is 100, we can make an equation - [tex]s^2=100[/tex]
- [tex]\sqrt{s^2}=\sqrt{100}[/tex]
- [tex]s=10[/tex]
Now that we know the value of s, we can plug it into the volume formula, [tex]s^3[/tex].
- [tex]10^3[/tex]
- [tex]10 \cdot 10 \cdot 10[/tex]
- [tex]1000[/tex]
So the volume is [tex]1000 \ \text{cm}^3[/tex].
Hope this helped!
