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?
each side is the cube root of 1000
To solve this problem, we need to find the increase in length for each side of the original cube to achieve a volume of 2,000 cubic inches.
The formula to find the volume of a cube is V = s^3, where V is the volume and s is the length of each side.
Let's start by calculating the volume of the original cube:
V_original = s^3 = 10^3 = 1,000 cubic inches.
Now we need to find the increase in volume required:
Increase_in_volume = Target_volume - V_original = 2,000 - 1,000 = 1,000 cubic inches.
Since the new cube has increased in volume, we can consider the increase as x. Now, the volume of the new cube will be:
V_new = (s + x)^3.
We know that V_new = 2,000, so we can set up the equation:
(s + x)^3 = 2,000.
To solve for x, we need to take the cube root of both sides of the equation:
∛((s + x)^3) = ∛(2,000).
Taking the cube root, we get:
s + x = ∛(2,000).
Now, we can rearrange the equation to solve for x:
x = ∛(2,000) - s.
Plugging in the value of s (s = 10, in this case), we can calculate the increase in length for each side:
x = ∛(2,000) - 10 ≈ 4.76 - 10 ≈ -5.24.
Since we are looking for a positive increase, we can disregard the negative value:
Increase_in_length ≈ 5.24 inches.
Therefore, Denis should increase the length of each side of the original box by approximately 5.24 inches to achieve a volume of 2,000 cubic inches.