Denis is designing a storage box in the shape of a cube.Each side of the box has a length of 10 inches. she needs more room anddecides to constructa largerbox in the shape of a cube with a volume of 2,000 cubic inches. By how many inches to the nearest tenth should she increse the length of each side of the original box?
x^3 = 2000
x = 12.6
now subtract 10
5 c 2
To solve this problem, we need to find the side length of the larger cube. Since the volume of a cube is given by the formula V = s^3, where V is the volume and s is the side length, we can set up an equation:
s^3 = 2000
To find the side length, we need to take the cube root of both sides of the equation:
s = ∛2000
To the nearest tenth, we can approximate:
s ≈ 12.6 inches
Now, to calculate by how many inches Denis should increase each side of the original cube, we subtract the original side length from the new side length:
Increase = 12.6 - 10
Increase ≈ 2.6 inches
Therefore, Denis should increase each side of the original cube by approximately 2.6 inches.