When you recreate a sculpture that is one-third the size of the original, the overall surface area of the sculpture will change accordingly. Here's how changes in the dimensions will affect the surface area:
1. **Original vs. Smaller Sculpture:**
- If the dimensions of the original sculpture are reduced to one-third of their size, the surface area of the smaller sculpture will also decrease.
- For example, if the original sculpture had a surface area of 100 square units, the smaller sculpture (one-third the size) would have a surface area of 1/3 * 100 = 33.3 square units.
2. **Surface Area and Dimensions Relationship:**
- Surface area is directly related to the dimensions of an object. When the dimensions change, the surface area changes proportionally.
- If you reduce the dimensions by a factor of "k" (in this case, k = 1/3 for one-third the size), the surface area will decrease by a factor of k^2.
- This means that the surface area of the smaller sculpture will be 1/3 * 1/3 = 1/9 of the surface area of the original sculpture.
3. **Understanding Proportional Changes:**
- The surface area of a sculpture is a two-dimensional measure, so changes in dimensions have a squared effect on the surface area.
- It's important to consider how reducing the size impacts not just the linear dimensions but also the overall surface area of the sculpture.
In summary, when you recreate a sculpture that is one-third the size of the original, the surface area of the smaller sculpture will decrease significantly compared to the original due to the proportional relationship between dimensions and surface area.
