https://file.aiquickdraw.com/mathbot/file/1727274580882ygbrwqfa.jpg

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!

A 1.25 inch cube of steel is placed in a surface grinding machine, and the vertical feed is set so that 0.0049 inch of metal is removed from the top of the cube at each cut. a. What is the volume of steel that is removed during each cut? Round to THREE decimal places. b. How many cuts are needed to reduce the volume of the cube by 0.1071875 cubic inch?

This problem involves calculating the volume of steel removed from a 1.25 inch cube using a surface grinding machine that removes 0.0049 inch of metal per cut. Learn how to compute the volume removed per cut and determine the number of cuts required to reduce the total volume by 0.1071875 cubic inches. Suitable for high school students in Grades 9-12.

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