d. After construction, the raised fire pit will have a volume of 0.99m^3 If the volume of the enlargement is 26.73m^3 what scale factor was used?

## Step 1: Find the ratio of the volumes<br />### The problem states the volume of the raised fire pit is $0.99 m^3$ and the enlarged volume is $26.73 m^3$. The ratio of the enlarged volume to the original volume is $\frac{26.73}{0.99}$.<br /><br />## Step 2: Calculate the ratio<br />### Dividing the enlarged volume by the original volume gives us $\frac{26.73}{0.99} = 27$. This represents the ratio of the volumes.<br /><br />## Step 3: Determine the scale factor<br />### The scale factor relates to the ratio of the corresponding lengths, not volumes. Since volume is a cubic measure (length $\times$ width $\times$ height), the scale factor is the cube root of the volume ratio. Therefore, the scale factor is $\sqrt[3]{27} = 3$.