if the length of each edge in a cube is increased by the same percent and the result was a cube that had 25% more volume than it originally had, by what percentage were the edges increased
To find the percentage by which the edges of the cube were increased, we need to start by understanding the relationship between the edge length and the volume of a cube.
In a cube, the volume is calculated by finding the cube of the edge length. So, if we denote the original edge length as "x," the original volume will be x^3.
Now, if each edge length is increased by the same percentage, we can represent the percentage increase as "y%." This means that the new edge length will be (x + (y/100)x), or (1 + (y/100))x.
The new volume, after increasing the edge length by y%, will be calculated by cubing the increased edge length: (1 + (y/100))^3 * x^3.
According to the problem, the new volume is 25% more than the original volume. Mathematically, we can express this as:
(1 + (25/100)) * x^3 = (1 + (y/100))^3 * x^3.
To find the percentage by which the edges were increased, we can now solve this equation for "y%."
(1 + (25/100))^3 * x^3 = (1 + (y/100))^3 * x^3
Cancelling out the x^3 on both sides of the equation, we have:
(1 + (25/100))^3 = (1 + (y/100))^3
Now, let's solve for y% by taking the cube root of both sides:
1 + (25/100) = 1 + (y/100)
25/100 = y/100
Hence, the edges of the cube were increased by 25%.