Let's break down the problem step-by-step based on the image and the questions:

Problem Details:

• A cube of steel has side lengths of 1.25 inches.
• Each time the grinding machine operates, it removes 0.0049 inches from the top.
• We need to compute the volume of steel removed after each cut and determine how many cuts are required to reduce the cube's volume by 0.1071875 cubic inches.

Part A: Volume Removed per Cut

The volume removed per cut is the area of the top face multiplied by the thickness of the material removed in each cut:

1. Top face area of the cube: $\text{Area} = \text{side} \times \text{side} = 1.25 \times 1.25 = 1.5625 \, \text{square inches}$

2. Volume removed in one cut: $\text{Volume} = \text{Area} \times \text{thickness of cut} = 1.5625 \times 0.0049 = 0.00765625 \, \text{cubic inches}$

Rounding to three decimal places: $\text{Volume removed per cut} = 0.008 \, \text{cubic inches}$

Part B: Number of Cuts to Reduce Volume by 0.1071875 Cubic Inches

To find the number of cuts required to remove 0.1071875 cubic inches of material, divide the target volume by the volume removed per cut:

$\text{Number of cuts} = \frac{\text{Target volume}}{\text{Volume per cut}} = \frac{0.1071875}{0.00765625} \approx 14$

So, 14 cuts are needed to remove the specified volume.

Would you like more details on any step of the solution? Here are some related questions:

1. What formula is used to calculate the volume of a cube?
2. How does changing the dimensions of a cube affect its volume?
3. What is the significance of rounding in such engineering problems?
4. How can similar problems be solved for different cube dimensions?
5. What happens if the amount removed per cut changes?

Tip: Always double-check units when calculating volumes, especially in practical applications like material removal!