if the length of each edge is of a cube is increased by 70%, then the percentage increase in the surface area of the cube is
To find the percentage increase in the surface area of the cube, let's first calculate the increase in the length of each edge and then calculate the increase in the surface area.
Let's assume the original length of each edge of the cube is 'x'.
The increase in the length of each edge is 70% of x, which is 0.7x.
After the increase, the new length of each edge is x + 0.7x = 1.7x.
The surface area of a cube is given by the formula: 6 * (side length)^2.
The original surface area of the cube is: 6 * x^2 = 6x^2.
The new surface area of the cube is: 6 * (1.7x)^2 = 6 * 2.89x^2 = 17.34x^2.
The increase in the surface area is: 17.34x^2 - 6x^2 = 11.34x^2.
Now let's calculate the percentage increase:
Percentage increase = (increase / original surface area) * 100%
= (11.34x^2 / 6x^2) * 100%
= (1.89) * 100%
= 189%
Therefore, the percentage increase in the surface area of the cube is 189%.