This is part of our
GRE Geometry Formulas project is the best complement to our
Official GRE Quant Book. It provides a cutting-edge, in-depth overview of all the math concepts to achieve 170 in the Quantitative Reasoning portion of the GRE. The book still remains our hallmark. However, the following chapters will give you a lot of tips, tricks, and shortcuts to make your quant preparation more robust and solid.
SOLIDSCubeA six–faced solid figure with all faces equal and adjacent faces mutually perpendicular is a cube.
If “a” be the edge of a cube,
1. The longest diagonal \(= a\sqrt{3}\) The face diagonal \(= a\sqrt{2}\)
2. Volume \(= a^3\)
3. Total surface area \(= 6 a^2\)
CUBOID or RECTANGULAR BOXIf a,b,c are the edges of a box,
1. The longest diagonal \(= \sqrt{(a^2 + b^2 + c^2)}\)
2. Surface area \(= 2 (ab + bc + ac)\)
3. Volume \(= abc\)
RIGHT CIRCULAR CYLINDERIf r is the radius of base and h is the height, then
[img]https://gre.myprepclub.com/forum/download/file.php?mode=view&id=14856&sid=39c06ed135b8f48a3a154da208f02f27[/img
1. Volume = \(\pi r^2 h\)
2. Curved surface area \(= 2 \pi rh\)
3. Total surface area \(= 2 \pi r (r + h)\)
4. If a rectangle of length L and breadth B is rotated about its length to form a cylinder, then \(L = 2 \pi R\) and \(B = h\).
5. If a rectangle of length L and breadth B is rotated about its breadth to form a cylinder, then \(B = 2 \pi R\) and \(L = h\)
RIGHT CIRCULAR CONER = radius of base
H = Height
L = slant height \(= \sqrt{(H^2 + R^2)}\)
1. Volume \(= \frac{1}{3} \times (\pi R^2H)\)
2. Curved surface Area \(= \pi R L\)
3. Total Surface Area \(= \pi R (R + L)\)
SPHERER = Radius
1. Volume \(= \frac{4}{3} \times \pi R^3\)
2. Surface Area \(= 4 \pi R^2\)
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