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Home > GC > Chapter 11 > Lesson 11.2.1 > Problem 11-76

11-76.

On your paper, draw a diagram of a square-based pyramid if the side length of the base is cm and the height of the pyramid is cm.  

  1. Find the volume of the pyramid.

    The formula to find the volume of a pyramid is 

    Calculate area of base:

    Use formula to calculate volume (a):

    Rectangular pyramid, with rectangle base, shaded, and sides labeled, x, and 9 cm, and distance from vertex to base, labeled 12 cm.

  1. If a smaller pyramid is similar to the pyramid in part (a), but has a linear scale factor of , find its volume.

    Find the volume of the smaller pyramid in one of two ways:
    Calculating from the dimensions or
    Using the ratio of volumes.

    Since the linear scale factor is  ,the ratio of the volume is ,

    Rectangular pyramid, with rectangle base, shaded, and side labeled, 1 third, x, and distance from vertex to base, labeled h.