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GMAT Solids

by ejkiv


July 19, 2015


GMAT Solids are simply 3-dimensional shapes and are one area where people tend to struggle because they try to memorize a set of formulas for the two things you might have to calculate for solids: surface area and volume. However, this section does not have to be difficult. A small bit of logic can help you sift through all of the formulas. Really the only two solids that are tested on the GMAT, in terms of formulas, are rectangular solids (including cubes) and cylinders. You may come across some spacial relationship problems with cones, sphere or pyramids, but you will not have to calculate the value of any components.

Surface area: the sum of the area of the faces of a solid

Volume: the amount of 3-dimensional space in a solid, or its capacity

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CYLINDER

Let’s look at the cylinder first. While we will talk about the formulas, it is best to think about this (and other) 3-dimensional shapes with a bit of logic. For surface area, there are 2 circles on the top and bottom and a rectangle that makes up the height. You may ask yourself how this is a rectangle, but if you curl a piece of paper you will see that it makes a cylinder. So, the area of that portion of the cylinder is simply b * h, where the base is the circumference of the circle at one base and the height is just the height of the cylinder. In formula terms:

Surface Area = 2πr^2 + dπh

Volume = πr2h

GMAT Solids - cylinderThe πr^2 represents the area of one of the circles at the base (you multiply that by 2 to calculate both sides). πdh is the circumference of the circle multiplied by the height.

For volume, you need to calculate the area of one side of the 3D object and multiply that value by the height. This principle will hold for all 3D objects. For the cylinder above, that means calculating the area of the circle and multiplying it by the height, or π(r^2)h.

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CUBE

The cube is probably the easiest solid to remember because all of the sides are the exact same. Thus, the surface area is 6 (the number of faces) times s^2, and the volume is s^2.

GMAT Solids - Cube

Surface Area = 6s^2

Volume = s^3

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RECTANGULAR SOLID

The cube is probably the easiest solid to remember because all of the sides are the exact same. Thus, the surface area is 6 (the number of faces) times s^2, and the volume is s^2.

GMAT Solids - Rectangular Solids

Surface Area = 2lw + 2lh + 2wh

Volume = lwh

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