Denise is designing a storage box in 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 a shape of a cube with a volume of 2000 cubic inches.By how many inches, to the nearest tenth ,should she increase the length of each side of the original box ?
2000^(1/3) = 12.6
12.6 - 10 = 2.6
To find out how much Denise should increase the length of each side of the original box, we need to calculate the volume of the original box and compare it to the desired volume of 2000 cubic inches.
The volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of each side.
Given that each side of the original box has a length of 10 inches, we can calculate its volume:
V_original = 10^3
= 1000 cubic inches
To find the difference in volume between the original box and the desired volume, we subtract the original volume from the desired volume:
Difference = Desired volume - Original volume
= 2000 - 1000
= 1000 cubic inches
Now, we need to find the increase in length of each side that would result in a difference of 1000 cubic inches in volume.
Since the volume of a cube is directly proportional to the cube of its side length, we can set up a proportion:
(V_increase / V_original) = (s_increase / s_original)^3
Substituting the given values, we have:
(1000 / 1000) = (s_increase / 10)^3
Simplifying the equation, we get:
1 = (s_increase / 10)^3
Taking the cube root of both sides, we find:
1^(1/3) = (s_increase / 10)^(3/3)
1 = (s_increase / 10)
To isolate s_increase, we multiply both sides by 10:
10 = s_increase
Therefore, Denise should increase the length of each side of the original box by 10 inches to obtain a larger box with a volume of 2000 cubic inches.