Denise 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 and decides to construct a larger box in the shape of a cube with a volume of 2,000 cubic inches. By how many inches, to the nearest tenth, should she increase the length of each side of the original box?

What number cubed = 2000? (12.6)

Subtract that number from 10 inches.

2.6

To find out by how many inches Denise should increase the length of each side of the original box, we need to calculate the difference between the volume of the larger box and the volume of the original box.

The volume of a cube is calculated by multiplying the length of one side by itself three times (side * side * side).

Let's first find out the volume of the original box with sides of length 10 inches:
Volume of the original box = 10 inches * 10 inches * 10 inches = 1000 cubic inches.

Now, we can calculate the difference in volumes:
Difference in volumes = Volume of the larger box - Volume of the original box = 2000 cubic inches - 1000 cubic inches = 1000 cubic inches.

Since we want to increase the length of each side by the same amount, we need to calculate the cube root of the difference in volumes. The cube root will give us the increase in length of each side.

Let's calculate the cube root of 1000 cubic inches to find the increase in length:
Cube root of 1000 cubic inches ≈ 10.0 inches.

Therefore, Denise should increase the length of each side of the original box by approximately 10 inches.

8.5