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To find the volume of the solid shown in the diagram, we need to calculate the volumes of both the trapezoidal prism and the semicircular prism and then sum them.

### 1. Volume of the Trapezoidal Prism
The volume \( V_1 \) of a prism can be calculated using the formula:

\[
V_1 = \text{Area of the cross-section} \times \text{Length}
\]

Given:
- Area of the cross-section of the trapezoidal prism = 520 cm²
- Length of the trapezoidal prism = 70 cm

\[
V_1 = 520 \, \text{cm}^2 \times 70 \, \text{cm} = 36400 \, \text{cm}^3
\]

### 2. Volume of the Semicircular Prism
The volume \( V_2 \) of the semicircular prism can be calculated similarly, but first, we need to find the area of the semicircular cross-section.

The formula for the area \( A \) of a semicircle is:

\[
A = \frac{1}{2} \pi r^2
\]

where \( r \) is the radius.

From the diagram:
- Diameter of the semicircle = 26 cm (which is the same as the height of the trapezoidal prism)
- Therefore, the radius \( r \) is 13 cm.

\[
A = \frac{1}{2} \times \pi \times 13^2 = \frac{1}{2} \times \pi \times 169 \approx 265.64 \, \text{cm}^2
\]

Now, the volume \( V_2 \) of the semicircular prism:

\[
V_2 = \text{Area of the semicircle} \times \text{Length}
\]

Given the length is also 70 cm:

\[
V_2 = 265.64 \, \text{cm}^2 \times 70 \, \text{cm} \approx 18594.8 \, \text{cm}^3
\]

### 3. Total Volume of the Solid
The total volume \( V \) of the solid is the sum of the volumes of the trapezoidal prism and the semicircular prism:

\[
V = V_1 + V_2 = 36400 \, \text{cm}^3 + 18594.8 \, \text{cm}^3 = 54994.8 \, \text{cm}^3
\]

So, the volume of the solid is **54994.8 cm³**.

Would you like more details on this, or do you have any other questions?

Here are some related questions you might find useful:
1. How do you find the surface area of a trapezoidal prism?
2. What is the difference between a prism and a pyramid?
3. How do you calculate the surface area of a composite solid?
4. How do you convert volume from cubic centimeters to liters?
5. What is the significance of the radius in calculating the area of a semicircle?
6. How does the length of the prism affect its volume?
7. What are some real-life applications of calculating the volume of composite solids?
8. How do you calculate the cost of painting the surface of a solid?

**Tip:** When working with composite solids, always break them down into simpler shapes for easier calculation.

Learn how to find the volume of a solid composed of a trapezoidal prism and a semicircular prism. Detailed step-by-step solution provided, including formulas for calculating the volumes of prisms and areas of semicircles. Suitable for Grades 7-9.

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