If the surface area of a cylinder with a radius of 4 inches and a height of 10 inches is equal to the surface area of a cube, which of the following is approximately equal to the length of one of the cube's edges? A. 3 B. 4 C. 5 D. 6 E. 8
(E) The first step in answering this question, is to determine the surface area of the cylinder and then set it equal to the surface area of the cube.
The cylinder can be broken down into two circular caps and a rectangular body whose length is equal to the circumference of each circular cap, and whose height is given. GMAT students should be familiar with taking areas of circles and rectangles. Each circular cap will have a surface area of: 4² × π, or 16π. Since we have two such caps, the sum of their areas must be equal to 32π square inches.
Next, we want to determine the surface area of the cylindrical body. The latter is equal to the circumference of the circle multiplied by height, 8π × 10 = 80π square inches.
So, the cylindrical surface area is equal to the sum of the areas we found: 80π + 32π = 112π square inches.
The next task requires that we set the surface area equal to the surface area of a cube. For now, let us choose the edge length of the cube to be x. The surface area of the cube is equal to the product of the number of faces and the area of each face (recall that each face of a cube is a square): 6x².
We set the two quantities equal to each other: 6x² = 112π. We can now solve this equation by dividing both sides by 6 and taking the square root of both sides: x = √(112π / 6).
Since the question asks us to approximate, we can let π equal 3. After the substitution we are left with √56, which is approximately equal to 8 or answer choice (E). 
The solution is incorrect as Surface area of cylinder is 2πr² + 2πrh where r is radius and h is height.
Your solution incorrectly calculates area of cylinderical body by not considering the height.
