A frustum of height 4 is part of a larger pyramid of height 6. What is the ratio of the volume of the frustum to the volume of the pyramid?

Since the smaller pyramid's height is  6 and the larger pyramid's height is 12, the scale factor is 6/12=1/2

The scale factor for the base would be (1/2)^2 (since we're multiplying the sides, and each of them has a scale factor of 1/2)=1/4

For the volume, since we add another side with scale factor 1/2, we multiply 1/4 by 1/2 to get 1/8

Step-by-step explanation:

Height (h₁) of one square pyramid = 12 m

A similar pyramid has a height h₂ = 6 m

(a)  Therefore scale factor of smaller pyramid to the larger pyramid =  =  =  1 : 2

(f)   Since ratio of the sides of smaller to larger pyramid is 1 : 2

so ratio of area of the bases =  =  

=  

(g)  Ratio of volume of smaller to larger pyramid

=  =  

(h)  Since  =  and V₁ = 400 m³

So   =  ⇒  =  

V₂ =  = 50 m³