Question 1192389
**1. Find the Volume of the Cuboid**

* **Original Volume (V):**
   V = Base Area × Height 
   V = x² × (2x + 1)
   When x = 10 cm:
   V = 10² × (2 * 10 + 1) 
   V = 100 × 21 
   V = 2100 cubic cm

**2. Approximate Increase in Volume**

* **Use Differentials:**
   * Volume (V) = x² * (2x + 1) = 2x³ + x²
   * dV/dx = 6x² + 2x 
   * Approximate change in volume (dV) ≈ (dV/dx) * dx 
      where dx is the change in x (0.05 cm in this case)
   * dV ≈ (6 * 10² + 2 * 10) * 0.05 
   * dV ≈ (600 + 20) * 0.05 
   * dV ≈ 31 cubic cm

**3. Approximate Volume when x = 10.05 cm**

* **Approximate New Volume:**
   * New Volume ≈ Original Volume + Approximate Increase in Volume
   * New Volume ≈ 2100 cubic cm + 31 cubic cm 
   * New Volume ≈ 2131 cubic cm

**Therefore:**

* **Approximate increase in volume:** 31 cubic cm
* **Approximate volume when x = 10.05 cm:** 2131 cubic cm

This method provides an approximation of the volume change using differentials. For a more precise calculation, you could directly calculate the volume at x = 10.05 cm and compare it to the original volume.