The volume of the original cube is 1000 cubic units.
What is volume of cube?
The volume of a cube is equal to the product of length, width and height of a cube.
Let the length of side of the original cube = L
The surface area of the original cube A₁ = 6 L²
When increase the side length of a certain cube by 4
The surface area of the increased cube A₂ = 6 (L + 4)²
The surface area increases by 576
So, 6(L + 4)² - 6 L² = 576
6(L² + 16 + 8L) - 6 L² = 576
Divided by 6 both the sides,
L² + 16 + 8L - L² = 96
16 + 8L = 96
8L = 96 - 16
8L = 80
L = 80/8
L = 10
So, the length of side of the original cube = L = 10 units
The volume of the original cube = L³
The volume of the original cube = (10)³
The volume of the original cube = 1000 cubic units
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