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### The circled question from **Question 4** asks to:
**a) Identify the total volume of the block**.

This is a composite solid that consists of:
1. A **rectangular cuboid** with dimensions \( 10 \, \text{cm} \times 8 \, \text{cm} \times 5 \, \text{cm} \).
2. A **cylindrical hole** drilled through the block with a diameter of \( 6 \, \text{cm} \) and height of \( 8 \, \text{cm} \) (the same height as the cuboid).

### Steps to solve:
1. **Volume of the cuboid**:
   \[
   V_{\text{cuboid}} = \text{length} \times \text{width} \times \text{height} = 10 \, \text{cm} \times 8 \, \text{cm} \times 5 \, \text{cm} = 400 \, \text{cm}^3
   \]

2. **Volume of the cylindrical hole**:
   The formula for the volume of a cylinder is \( V = \pi r^2 h \), where:
   - Radius \( r = \frac{6}{2} = 3 \, \text{cm} \),
   - Height \( h = 8 \, \text{cm} \).
   
   So,
   \[
   V_{\text{cylinder}} = \pi \times 3^2 \times 8 = \pi \times 9 \times 8 = 72\pi \, \text{cm}^3 \approx 226.2 \, \text{cm}^3
   \]

3. **Total volume of the block**:
   To get the total volume, subtract the volume of the cylindrical hole from the volume of the cuboid:
   \[
   V_{\text{total}} = V_{\text{cuboid}} - V_{\text{cylinder}} = 400 - 72\pi \approx 400 - 226.2 = 173.8 \, \text{cm}^3
   \]

So, the total volume of the block is approximately **173.8 cm³**.

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Would you like further details on any part of this problem? Here are five related questions you might find interesting:

1. How do you find the surface area of a cuboid?
2. What would the total surface area of this block be, considering the cylindrical hole?
3. How do you calculate the volume of other composite solids?
4. How does the volume of a cone compare to that of a cylinder?
5. Can the volume of a cuboid be maximized for a fixed surface area?

**Tip**: When dealing with composite shapes, always break the problem into manageable parts by calculating each solid's properties separately before combining results.

Identify the total volume of the composite block that consists of a rectangular cuboid (10 cm × 8 cm × 5 cm) with a cylindrical hole (diameter 6 cm, height 8 cm) drilled through it.

Learn how to calculate the total volume of a composite block consisting of a rectangular cuboid (10 cm × 8 cm × 5 cm) and a cylindrical hole (diameter 6 cm, height 8 cm). This problem explores key geometry concepts such as the volume of cuboids and cylinders, using formulas like V = length × width × height and V = πr²h. Suitable for students in Grades 9-10.

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