Question

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?

Answer 1

To increase the volume of the original cube to 2,000 cubic inches, Denise should increase the length of each side by approximately 2.6 inches.

Step-by-step explanation:

To find the increase in length of each side of the original box, we need to calculate the length of each side of the larger box. Since the volume of the larger cube is given as 2,000 cubic inches, we need to find the side length that has a volume of 2,000 cubic inches.

Since the original cube has side lengths of 10 inches, we can use the formula for the volume of a cube, which is V = s^3, where V is the volume and s is the side length.

Given that the volume of the larger cube is 2,000 cubic inches, we can set up the equation 2,000 = s^3 and solve for s to find the increase in length.

Take the cube root of both sides of the equation: ∛2,000 = s

Using a calculator, we can find that ∛2,000 = 12.6 (rounded to one decimal place).

Therefore, Denise should increase the length of each side of the original box by approximately 2.6 inches (12.6 - 10) to achieve a volume of 2,000 cubic inches.