Question

Two similar pyramids have slant height of 4 and 6.1. Find the scale factor.2. If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?

Answer 1

1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:

`(6)/(4)=(3)/(2)\text{ or 1.5}`

So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.

2) For the Volume of the Pyramid, we can write out the formula below:

`V=(1)/(3)\cdot Ab\cdot h`

Since the scale factor is 1.5 Then we can state that

`\begin{gathered} V=(48)/((3)/(2)) \\ V=32 \end{gathered}`

the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.

3) Hence, the answers are:

1.k=1.5

2. 32 m³