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

step-by-step explanation:

4227473658779875563886538705958641728563470543621287463824132573847969p05749365273847906970680574936214

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it