hi honestly speaking i have no idea how to even start this problem but i know that a cube is to the 3rd power here is the problem
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?
I answered this two days ago. Are you the same person who asked it then?
Refer to:
http://www.jiskha.com/display.cgi?id=1265083826
no i am not the same person
To solve this problem, we can use the concept of volume of a cube.
The formula for the volume of a cube is V = s^3, where V represents the volume and s represents the length of each side of the cube.
In this problem, the original box has a side length of 10 inches. Therefore, its volume is V = 10^3 = 1,000 cubic inches.
Denis wants to construct a larger box with a volume of 2,000 cubic inches.
To find the increase in the length of each side of the original box, we need to calculate the difference between the desired volume and the volume of the original box.
Let's call the increase in length "x". So, the new side length will be 10 + x.
The volume of the new box will be (10 + x)^3.
Now, we can set up an equation:
(10 + x)^3 = 2,000
To solve this equation, we need to find the cube root of both sides to isolate the variable x.
Cube root of ((10 + x)^3) = cube root of 2,000
Simplifying:
10 + x = cube root of 2,000
Finally, solving for x:
x = cube root of 2,000 - 10
Using a calculator to find the cube root of 2,000, we get:
x ≈ 3.2
Therefore, Denis should increase the length of each side of the original box by approximately 3.2 inches to the nearest tenth.