To calculate the area of the cross-section of the container, we first need to understand the given shape from the image. However, due to the limited resolution, I'll guide you through a general approach to solve such a problem based on the typical structure of a container cross-section involving cylindrical and possibly other simple shapes.

Assumptions from Image Details

1. Top Cross-Section View: The image shows a top view of a cylindrical shape with a rectangular cutout (as commonly seen in the shape of a pill bottle, for instance).

2. Dimensions:

   • Cylindrical Part: The full circle has a radius of 15 cm.
   • Rectangular Cutout: Assuming the rectangular shape cuts through the cylinder's circular cross-section, with dimensions 12 cm by 6 cm.

Step-by-Step Calculation:

1. Calculate the Area of the Full Circle (Cylindrical part):

   $A_{\text{circle}} = \pi \times \text{radius}^2 = \pi \times (15)^2 = 225\pi \, \text{cm}^2$

2. Calculate the Area of the Rectangular Cutout:

   $A_{\text{rectangle}} = \text{length} \times \text{width} = 12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2$

3. Calculate the Area of the Cross-Section of the Container:

   Since the rectangle is a cutout from the circular area:

   $A_{\text{cross-section}} = A_{\text{circle}} - A_{\text{rectangle}}$

   Substituting the values:

   $A_{\text{cross-section}} = 225\pi - 72$

4. Final Answer in Exact Form and Approximate Numerical Form:

   $A_{\text{cross-section}} = 225\pi - 72 \, \text{cm}^2 \approx 633.56 \, \text{cm}^2 - 72 \, \text{cm}^2 = 561.56 \, \text{cm}^2$

Conclusion

The area of the cross-section of the container is approximately 561.56 cm².

Would you like more details or have any specific questions?

Additional Related Questions:

1. How would the cross-sectional area change if the radius of the cylindrical part increased by 5 cm?
2. What would be the volume of the container if the height is 30 cm?
3. How would you calculate the perimeter of the cross-sectional area?
4. How do variations in the shape of the cutout affect the cross-sectional area?
5. Can you compute the volume of a liquid that fills up to half the height of the container?

Tip:

Always double-check the dimensions and ensure that all units are consistent when performing calculations.