Five equal cubes, each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be

### Concept & Additive Volume When identical standard shapes are stacked or placed adjacently, their combined volume is simply the sum of their individual volumes. Forming a new cuboid by placing cubes adjacent to each other increases length while keeping breadth and height constant. $$V = \text{Number of cubes} \times \text{Volume of one cube}$$ ### Step-by-Step Solution 1. **Method 1: Direct Volume Addition** - Volume of one cube = $side^3 = 5^3 = 125 \text{ cm}^3$. - Since there are 5 identical cubes, the total volume = $5 \times 125 = 625 \text{ cm}^3$. 2. **Method 2: Cuboid Dimensions** - Placing 5 cubes of side $5 \text{ cm}$ in a row forms a cuboid. - Length ($L$) = $5 \times 5 = 25 \text{ cm}$. - Breadth ($B$) = $5 \text{ cm}$. - Height ($H$) = $5 \text{ cm}$. - Volume of cuboid = $L \times B \times H = 25 \times 5 \times 5 = 625 \text{ cm}^3$. ### Exam Strategy & Shortcut Do not recalculate physical dimensions unless asked for surface area. For total volume of identical adjacent objects, always use direct multiplication: $N \times a^3$. It is much faster and less error-prone. ### Common Pitfall Calculating surface area instead of volume, or mistakenly cubing the combined length ($25^3$) instead of properly multiplying length, breadth, and height. ### Final Answer Therefore, the correct answer is **625 cm³**.