Subjects geometry

Tank Fill Count 206E56

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1. **Stating the problem:** We want to find how many small tanks (each 4 ft by 4 ft) can be filled with the water from Part A. The small tank is a cube with side length 4 ft. 2. **Formula and rules:** To find how many small tanks can be filled, we need the volume of water from Part A and the volume of one small tank. - Volume of a cube (tank) = side³ = $4^3 = 64$ cubic feet. 3. **Intermediate work:** - Let $V_A$ be the volume of water from Part A (not given explicitly here). - Number of small tanks filled = $\frac{V_A}{64}$. Since the volume from Part A is not provided in this message, we cannot compute the exact number. Please provide the volume from Part A to continue. --- 4. **Hexagon transformations:** - Given hexagon ABCDEF with F midpoint of AE. - Transformations that map the hexagon into itself: A) Reflecting over AE: Since F is midpoint of AE, reflecting over AE will map the hexagon onto itself. B) Reflecting over CF: This depends on symmetry; generally, CF is not an axis of symmetry for an irregular hexagon. C) Rotating 90° clockwise around F: Unlikely to map irregular hexagon onto itself. D) Rotating 180° around F then reflecting over AE: Combination may map hexagon onto itself if symmetry exists. **Answer:** A and possibly D, but without more info, A is the sure transformation. --- **Summary:** - To answer the tank question, volume from Part A is needed. - For hexagon transformations, reflecting over AE (A) maps the hexagon onto itself.
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