If the edge of a cube is increase by 30% by how much is the surace area increased?

by 1.30^2 = 1.69 or 69%

To find out how much the surface area of a cube increases when its edge is increased by 30%, we can follow these steps:

Step 1: Understand the problem.
The problem states that the edge of a cube is increased by 30%. We need to determine the corresponding increase in the cube's surface area.

Step 2: Recall the formula for the surface area of a cube.
The surface area of a cube is given by the formula: SA = 6 * a^2, where "SA" represents the surface area and "a" represents the length of one edge.

Step 3: Calculate the new length of the cube's edge.
Since the edge is increased by 30%, we can calculate the new length as follows:
New Edge length = Original Edge length + (30% of Original Edge length)
= Original Edge length + (0.3 * Original Edge length)
= Original Edge length * (1 + 0.3)
= Original Edge length * 1.3

Step 4: Calculate the original and new surface areas.
Let's assume the original edge length is "x."
The original surface area (SA_1) is 6 * x^2.
The new edge length is 1.3x (as calculated in step 3).
The new surface area (SA_2) is 6 * (1.3x)^2.

Step 5: Calculate the increase in surface area.
To calculate the increase in surface area, we subtract the original surface area from the new surface area:
SA_increase = SA_2 - SA_1.

Let's calculate the increase in the surface area using an example:
Suppose the original edge length of the cube is 10 units.

Step 6: Substitute the values into the equations to calculate the increase.
Original Surface Area (SA_1) = 6 * (10^2) = 600 square units.

New Edge length = Original Edge length * 1.3 = 10 * 1.3 = 13 units.
New Surface Area (SA_2) = 6 * (13^2) = 1014 square units.

SA_increase = SA_2 - SA_1 = 1014 - 600 = 414 square units.

Therefore, if the edge of a cube is increased by 30%, the surface area is increased by 414 square units.

To find out the increase in surface area of a cube when its edge is increased by 30%, we need to follow these steps:

Step 1: Determine the original edge length of the cube.
Step 2: Calculate the original surface area of the cube.
Step 3: Calculate the new edge length after a 30% increase.
Step 4: Calculate the new surface area of the cube.
Step 5: Calculate the difference between the new and original surface areas to find the increase.

Let's go through the steps one by one.

Step 1: Determine the original edge length of the cube.
Let's assume the original edge length of the cube is "x" units (e.g., cm, m, etc.).

Step 2: Calculate the original surface area of the cube.
The formula to calculate the surface area of a cube is: SA = 6 * (edge length)^2.
So, the original surface area (SA1) is: SA1 = 6 * x^2.

Step 3: Calculate the new edge length after a 30% increase.
To find the new edge length, we need to increase the original length (x) by 30%.
The increase can be calculated by multiplying the original length (x) by 30/100 or 0.3.
So, the increase in length is: increase = 0.3 * x.
Therefore, the new edge length (x_new) is: x_new = x + increase = x + 0.3 * x = x(1 + 0.3) = 1.3x.

Step 4: Calculate the new surface area of the cube.
Using the new edge length (x_new), the new surface area (SA2) is: SA2 = 6 * (x_new)^2 = 6 * (1.3x)^2 = 6 * 1.69x^2 = 10.14x^2.

Step 5: Calculate the difference between the new and original surface areas.
To find the increase in surface area, we subtract the original surface area (SA1) from the new surface area (SA2).
Increase in surface area = SA2 - SA1
= 10.14x^2 - 6x^2
= 4.14x^2.

Therefore, the surface area of the cube is increased by 4.14 times the original surface area when its edge is increased by 30%.