Question

Pyramid P is similar to pyramid Q. The volume of pyramid P is 980 c m cubed, and the volume of pyramid Q is 3307.5 c m cubed. What is the scale factor that would enlarge pyramid P to the size of pyramid Q?

Answer 1

The scale factor is
`(3)/(2)`

Explanation:

The volume of the original prism is
`V_P=980cm^3`

The volume of the dilated prism is
`V_Q=3307.5cm^3`

Let the scale factor be
`k`.

To find the volume of the dilated prism, we multiplied by
`k^3`.

`\Rightarrow 980k^3=3307.5`

`\Rightarrow k^3=(3307.5)/(980)`

`\Rightarrow k^3=(27)/(8)`

`\Rightarrow k=\sqrt[3]{(27)/(8)}`

`\Rightarrow k=(3)/(2)`