Volume Formula for Rectangular Pyramids
The volume formula for rectangular pyramids is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume. For a rectangular pyramid with length l, width w, and height h, the volume equals one-third times l times w times h. For example, a pyramid with a 6 by 4 cm base and height 9 cm has volume one-third times 6 times 4 times 9 equals 72 cubic centimeters.
Key Concepts
For a rectangular pyramid with length $\ell$, width $w$, and height $h$, the volume is: $$V = \frac{1}{3}\ell wh$$.
Common Questions
What is the formula for the volume of a rectangular pyramid?
V equals one-third times l times w times h, where l is the length, w is the width, and h is the perpendicular height from base to apex.
How is rectangular pyramid volume related to rectangular prism volume?
A rectangular pyramid has exactly one-third the volume of a rectangular prism with the same base dimensions and height. This is why the formula includes the one-third factor.
What is the height used in the rectangular pyramid volume formula?
The height h is the perpendicular distance from the apex straight down to the base, not the slant height along a lateral face.
What textbook covers rectangular pyramid volume in Grade 7?
Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume covers the volume formula for rectangular pyramids.