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?
She goes from 1000 in^3 volume to 2000 in^3. The side length increases from 10 to the cube root of 2000, which is 12.60 inch.
Side length increases by 2.6 inches.
thank you so much!
Why did the cube go on a diet? Because it wanted to get a-little-bit more square meals!
To find the increase in length of each side of the original box, we need to calculate the cube root of the desired volume increase. Let's do the math:
Cube root of 2000 ≈ 12.7
So Denise should increase the length of each side of the original box by approximately 12.7 inches to achieve a volume of 2,000 cubic inches.
To find out how much 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 cubing the length of one side. In this case, the original box has sides with a length of 10 inches, so its volume is 10^3 = 1000 cubic inches.
The volume of the larger box is given as 2000 cubic inches.
To find the difference in volume, we subtract the volume of the original box from the volume of the larger box: 2000 - 1000 = 1000 cubic inches.
Since all sides of the box are equal in length, we can calculate the increase in length of one side by taking the cube root of the volume difference. In this case, the cube root of 1000 is approximately 10.
Therefore, Denise should increase the length of each side of the original box by approximately 10 inches to achieve a volume of 2000 cubic inches.