3-Dimensional Shapes

Rules

The volume of a non-tapering 3-dimensional object is the area of the base multiplied by the height.

Irregular objects and those which “taper” - or are not the same from the bottom to the top - are typically not tested on the GRE. However, for block-shaped objects, the formula is simply length(width)(height). However, there are two key tapering objects which do have simple formulas and could be tested - cones, and spheres.

The volume of a cone is one third of the area of the base multiplied by the height.

The area of the base will utilize the same formula for a circle.

The volume of a sphere is ${\displaystyle {\frac {4}{3}}\pi r^{3}}$ . A “sphere” is a round three-dimensional object, such as a ball or a globe.

Practice

1. A cereal box (left) has a volume of 225. If the dimensions of the face of the cereal box are 18 and 5, what is the depth of the cereal box?

2. A cylinder (right) has a diameter of 22 and a height of 45. What is the volume of the cylinder?

3. A soccer ball has a diameter of 12. A tennis ball has a diameter of 2. The volume of the tennis ball is what percentage of the volume of the soccer ball?