Question

(e) The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Determine each of the following, showing all your work and reasoning.

(a) Scale factor of the smaller pyramid to the larger pyramid in simplest form

(f) Ratio of the areas of the bases of the smaller pyramid to the larger pyramid

(g) Ratio of the volume of the smaller pyramid to the larger

(h) Volume of the smaller pyramid

Answer 1

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

Answer 2

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 =
`(h_(2) )/(h_(1))` =
`(6)/(12)` = 1 : 2

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

so ratio of area of the bases =
`((1)^2)/((2)^2)` =
`(1)/(4)`

`(A_(2))/(A_(1))` =
`(1)/(4)`

(g) Ratio of volume of smaller to larger pyramid

`(V_(2))/(V_(1))` =
`((1)^3)/((2)^3)` =
`(1)/(8)`

(h) Since
`(V_(2))/(V_(1))` =
`(1)/(8)` and V₁ = 400 m³

So
`(V_(2))/(V_(1))` =
`(1)/(8)` ⇒
`(V_(2))/(400)` =
`(1)/(8)`

V₂ =
`(400)/(8)` = 50 m³