Question

I'd appreciate any help I can get! :) A gold statue has a diameter of 60 inches and a height of 80 inches. It has a total volume of 320 inches cubed. The replica is proportional to the statue. The replica's height is 100 inches. What is the replica's volume?

Answer 1

Volume of replica = 625 cubic inches

Explanation:

Height of the gold statue = 80 inches

Volume of the gold statue = 320 cubic inches

Height of the replica = 100 inches

Dimensional scale factor =
`(\frac{\text{Dimension of the replica}}{\text{Dimension of the original statue}})`

=
`(100)/(80)`

= 1.25

Volume scale factor =
`\frac{\text{Volume of replica}}{\text{Volume of original}}`

Since, volume scale factor = (Dimensional scale factor)³

`\frac{\text{Volume of replica}}{\text{Volume of original}}=(1.25)^3`

Volume of replica = (1.25)³ × Volume of original statue

= (1.25)³ × 320

= 625 cubic inches