Answer:
1000 cubic units
Step-by-step explanation:
In order to find the volume, we must find the side length. We can do this through the surface area. The surface area of a cube can be found using the following formula.
[tex]A=6s^2[/tex]
We know the surface area is 600 square units. We can substitute 600 un² in for A.
[tex]600 un^2=6s^2[/tex]
We want to find s, the side length. Therefore, we must isolate s.
6 is being multiplied by s². The inverse of multiplication is division. Divide both sides of the equation by 6.
[tex]600 un^2/6=6s^2/6[/tex]
[tex]600 un^2/6=s^2[/tex]
[tex]100 un^2=s^2[/tex]
s is being squared. The inverse of a square is the square root. Take the square root of both sides of the equation.
[tex]\sqrt{100 un^2} =\sqrt{s^2}[/tex]
[tex]\sqrt{100 un^2}=s\\[/tex]
[tex]10 un=s[/tex]
The side length is 10 units.
Now we can find the volume using the following formula.
[tex]V=s^3[/tex]
The side length is 10 units. Substitute 10 un in for s.
[tex]V= (10 un)^3[/tex]
Solve the exponent.
⇒ (10 un)³= 10 un * 10 un * 10 un= 100 un²* 10 un= 1000 un³
[tex]V= 1000 un^3[/tex]
The volume is 1000 cubic units.
