Kelly glues unit cubes together by matching a $$ 1 imes 1 $$ face to another $$ 1 imes 1 $$ face to create the open-top box shown. The box has a bottom made of $$ 1 imes 1 $$ cubes. What is the total number of cubes used to create this box?

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Kelly glues unit cubes together by matching a $$ 1 	imes 1 $$ face to another $$ 1 	imes 1 $$ face to create the open-top box shown. The box has a bottom made of $$ 1 	imes 1 $$ cubes. What is the total number of cubes used to create this box?

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To determine the total number of unit cubes used to create Kelly's open-top box, let's break down the construction assuming a typical open-top rectangular box structure.

1. **Bottom Layer:**
   - The bottom of the box is made up of a layer of $$1 \times 1$$ unit cubes. Suppose the bottom is a $$3 \times 3$$ grid. This layer would consist of:
     $$
     3 \times 3 = 9 \text{ unit cubes}
     $$

2. **Walls:**
   - Since the box is open-top, we need to add the walls around the perimeter. Each wall would be one unit high. For a $$3 \times 3$$ base, each of the four sides would require 2 additional unit cubes (excluding the corners which are already part of the bottom layer):
     $$
     4 \text{ sides} \times 2 \text{ unit cubes per side} = 8 \text{ unit cubes}
     $$

3. **Total Count:**
   - Adding the bottom layer and the walls together:
     $$
     9 \text{ (bottom)} + 8 \text{ (walls)} = 17 \text{ unit cubes}
     $$

Therefore, the total number of unit cubes used to create the open-top box is **17**.

**Answer:** 17
The box uses a total of 17 unit cubes.

Kelly glues unit cubes together by matching a \( 1 \times 1 \) face to another \( 1 \times 1 \) face to create the open-top box shown. The box has a bottom made of \( 1 \times 1 \) cubes. What is the total number of cubes used to create this box?

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