The length of each edge of a cube is increased by 20%. What is the percent increase in the surface area of the cube?

Step 1: Understand the problem A cube has 6 equal sides. If the length of each edge of a cube is increased by 20%, then the surface area of each face of the cube will also increase. We need to find out by what percent the total surface area increases.

Step 2: Recall the formula for the surface area of a cube The surface area (A) of a cube with side length (s) is given by the formula A = 6s^2.

Step 3: Calculate the new side length If the length of each edge of the cube is increased by 20%, then the new side length (s') is 1.20s.

Step 4: Calculate the new surface area Substitute s' into the formula for the surface area of a cube to get the new surface area (A') which is A' = 6(1.20s)^2 = 6(1.44s^2) = 8.64s^2.

Step 5: Calculate the percent increase in the surface area The percent increase in the surface area is given by the formula ((A' - A) / A) * 100%. Substituting A' = 8.64s^2 and A = 6s^2 into this formula gives ((8.64s^2 - 6s^2) / 6s^2) * 100% = (2.64s^2 / 6s^2) * 100% = 44%.

So, the surface area of the cube increases by 44% when the length of each edge is increased by 20%.

Step 1: Understand the problem A cube has 6 equal sides. If the length of each edge of a cube is increased by 20%, we need to find out how much the surface area increases.

Step 2: Recall the formula for the surface area of a cube The surface area of a cube is given by the formula 6a^2, where a is the length of an edge.

Step 3: Calculate the new length of an edge If the length of each edge is increased by 20%, the new length is 1.20a.

Step 4: Calculate the new surface area Substitute 1.20a into the formula for the surface area of a cube to get the new surface area: 6*(1.20a)^2 = 6*1.44a^2 = 8.64a^2.

Step 5: Calculate the percent increase in the surface area The percent increase in the surface area is given by the formula ((new - old) / old) * 100%. Substituting the old surface area (6a^2) and the new surface area (8.64a^2) into this formula gives ((8.64a^2 - 6a^2) / 6a^2) * 100% = (2.64a^2 / 6a^2) * 100% = 44%.

So, the surface area of the cube increases by 44% when the length of each edge is increased by 20%.