https://r2.erweima.ai/mathbot/image/1725950431334ywy2k1gd.jpg

The image contains two sets of questions, each asking to calculate the volume of different prisms. Let’s tackle the problems one by one.

### Formula for Volume of a Prism:
The volume \( V \) of a prism is given by the formula:
\[
V = A \times h
\]
where:
- \( A \) is the area of the cross-sectional shape (the face).
- \( h \) is the length of the prism.

Let's go step by step to solve the prisms in **Question 1**.

---

### **Question 1:**

1. **(a)** Rectangular prism:
   - Dimensions: \( 3 \, \text{cm} \times 4 \, \text{cm} \times 6 \, \text{cm} \)
   - Volume:
   \[
   V = 3 \times 4 \times 6 = 72 \, \text{cm}^3
   \]

2. **(b)** Rhombus prism:
   - Cross-sectional area: Base = 6 cm, Height = 5 cm
   \[
   A = \text{Base} \times \text{Height} = 6 \times 5 = 30 \, \text{cm}^2
   \]
   - Length = 20 cm
   - Volume:
   \[
   V = A \times \text{Length} = 30 \times 20 = 600 \, \text{cm}^3
   \]

3. **(c)** Triangular prism:
   - Cross-sectional area: Base = 7 m, Height = 5 m
   \[
   A = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 7 \times 5 = 17.5 \, \text{m}^2
   \]
   - Length = 4 m
   - Volume:
   \[
   V = A \times \text{Length} = 17.5 \times 4 = 70 \, \text{m}^3
   \]

4. **(d)** Rectangular prism:
   - Dimensions: \( 2 \, \text{m} \times 1.1 \, \text{m} \times 40 \, \text{cm} \)
   - Convert: 40 cm = 0.4 m
   - Volume:
   \[
   V = 2 \times 1.1 \times 0.4 = 0.88 \, \text{m}^3
   \]

5. **(e)** Trapezoidal prism:
   - Trapezoid area: Parallel sides = 7 cm, 5.5 cm; Height = 8 cm
   \[
   A = \frac{1}{2} \times (7 + 5.5) \times 8 = \frac{1}{2} \times 12.5 \times 8 = 50 \, \text{cm}^2
   \]
   - Length = 8 cm
   - Volume:
   \[
   V = 50 \times 8 = 400 \, \text{cm}^3
   \]

6. **(f)** Triangular prism:
   - Cross-sectional area: Base = 6 cm, Height = 9 cm
   \[
   A = \frac{1}{2} \times 6 \times 9 = 27 \, \text{cm}^2
   \]
   - Length = 12 cm
   - Volume:
   \[
   V = 27 \times 12 = 324 \, \text{cm}^3
   \]

7. **(g)** Trapezoidal prism:
   - Trapezoid area: Parallel sides = 13 cm, 5 cm; Height = 12 cm
   \[
   A = \frac{1}{2} \times (13 + 5) \times 12 = \frac{1}{2} \times 18 \times 12 = 108 \, \text{cm}^2
   \]
   - Length = 22 cm
   - Volume:
   \[
   V = 108 \times 22 = 2376 \, \text{cm}^3
   \]

8. **(h)** Triangular prism:
   - Cross-sectional area: Base = 25 cm, Height = 8 cm
   \[
   A = \frac{1}{2} \times 25 \times 8 = 100 \, \text{cm}^2
   \]
   - Length = 40 cm
   - Volume:
   \[
   V = 100 \times 40 = 4000 \, \text{cm}^3
   \]

9. **(i)** Trapezoidal prism:
   - Trapezoid area: Parallel sides = 11 cm, 9 cm; Height = 14 cm
   \[
   A = \frac{1}{2} \times (11 + 9) \times 14 = \frac{1}{2} \times 20 \times 14 = 140 \, \text{cm}^2
   \]
   - Length = 15 cm
   - Volume:
   \[
   V = 140 \times 15 = 2100 \, \text{cm}^3
   \]

---

If you'd like, I can proceed with the volumes for **Question 2**.

Would you like more details or explanations for any part of this? Here are five related questions for you to think about:

1. How do you calculate the cross-sectional area of a prism if the face is a circle?
2. Why is the formula for volume the same regardless of the shape of the cross-section?
3. What happens to the volume of a prism if its length doubles but its cross-sectional area stays the same?
4. Can you explain how to calculate the volume of a cylinder?
5. How would you calculate the surface area of these prisms?

**Tip:** Always ensure the units are consistent when performing volume calculations. If dimensions are given in different units (e.g., meters and centimeters), convert them before solving.

Calculate the volume of each prism provided in the image for Questions 1 and 2.

Calculate the volume of various prisms, including rectangular, triangular, and trapezoidal prisms. This problem set covers key geometry concepts, such as area calculations for cross-sections and applying the prism volume formula. Suitable for students in Grades 8-10.

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