Surface area is the sum of all of the areas on the surface of an object. If you can solve for the area of circles, rectangles, and triangle, you can find the surface area of all three dimensional objects tested on the GMAT.

Rectangular Surface Area

SA for a Rectangular Solid = Sum the areas of all object faces.

surface-area-example1

SA = 2 ( 4 x 3 ) + 2 ( 6 x 3 ) + 2 ( 6 x 4 ) = 108

The area of the front surface is 6 x 4 = 24 , since there are two of them, a front and a back, we multiply this by 2. The area of the side is 4 x 3 = 12, since there are two sides, we multiply this by 2. The top surface area is 6 x 3 = 18. Again, since there is a top and bottom, we multiply this by 2. Sum all areas together and we get the final answer: 108

Cylinder surface area

Cylinder surface area can be calculated using the formula:

SA = 2 (πr²) + 2πrh

where r is the radius and h is the height of the cylinder

The derivation of this equation is actually very intuitive. We are simply adding together the areas of every surface on the cylinder. We begin by summing the areas of the top and bottom circles. Then, imagine the cylinder is like a soda can, if the top and bottom are cut off and the middle area is unfolded flat, it forms a rectangle. The length and width of the rectangle will be the height of the cylinder and the circumference of the circle will be the width. Multiply length and width together and sum with the area of the top and bottom circles to find the surface area of the cylinder.

Example

surface-area-example2

SA = 2 (π) + ( 6 x 2π) = 14π


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