Question

GRE Mini-Tutorial: Solid Geometry

Answer 1

\({\bf{Formula~List:}}\) thankfully there's not too much to remember here, but as usual be careful with units

volume of a rectangular prism: height*length*width
special case: volume of a cube, where the dimensions are equal = s^3 where s is the side length
diagonal: sqrt(l^2 + w^2 + h^2) that cuts through the box from corner to opposite-corner

these formulas will only be accurate if all the dimensions are in the same units

volume of a cylinder: bh, or pi*r^2 * h
surface area = 2pi*r*h + 2pi*r^2
imagine unrolling the cylinder into a rectangle and two attached circles
the rectangular part has length equal to the circumference of the circle (hence the 2pir part) and width equal to the height of the cylinder (hence, the h), then you add the two circular sides

Answer 2

these two are much less likely to be tested but just in case:

> volume of a sphere: (4/3)pi*r^3
> surface area of a sphere: 4pi*r^2

> volume of a cone: (1/3) of the cylinder with the same radius and height
> surface area of a cone: *** very unlikely to be tested ***

> volume of a square pyramid: (1/3) of the prism with the same base and height
> surface area of rectangular pyramid: apply the triangle area formula to the four triangular sides, then add the base

Answer 3

Anyway, that's the end of my tutorial, I hope it was a helpful resource. Source material is the ETS Data Interpretation Sample Questions website and the 19th edition Barron's prep book for the new GRE.

Answer 4

it's in my review book so just for convenience sake: A cube has 6 faces, 8 vertices and 12 edges.