The problem appears to involve a composite solid that consists of two cylinders. The image shows a smaller, vertical cylinder on top of a larger, horizontal cylinder. The task is to find the total volume of this composite solid.

Given:

• Small cylinder (orange):

  • Radius $r_1 = 6 \, \text{cm}$
  • Height $h_1 = 10 \, \text{cm}$

• Large cylinder (blue):

  • Radius $r_2 = 10 \, \text{cm}$
  • Height $h_2 = 2 \, \text{cm}$

Steps to solve:

1. Calculate the volume of the smaller (orange) cylinder: The volume $V_1$ of a cylinder is given by: $V_1 = \pi r_1^2 h_1$ Substituting the values: $V_1 = \pi (6)^2 (10) = 360\pi \, \text{cm}^3$

2. Calculate the volume of the larger (blue) cylinder: The volume $V_2$ of the large cylinder is: $V_2 = \pi r_2^2 h_2$ Substituting the values: $V_2 = \pi (10)^2 (2) = 200\pi \, \text{cm}^3$

3. Find the total volume of the composite solid: Add the volumes of both cylinders: $V_{\text{total}} = V_1 + V_2 = 360\pi + 200\pi = 560\pi \, \text{cm}^3$

Final Answer:

The total volume of the composite solid is $\boxed{560\pi \, \text{cm}^3}$.

Would you like more details on any part of this solution, or do you have any questions?

Here are some related questions to expand your understanding:

1. How do you calculate the surface area of the composite solid?
2. What would be the volume if the height of the small cylinder were doubled?
3. How would the total volume change if the radius of the large cylinder were increased by 50%?
4. If the material of the small cylinder has a density of 2 g/cm³, what would be its mass?
5. How does the total volume change if both the height and radius of the small cylinder are halved?

Tip: Always ensure units are consistent when calculating volume, area, or any other physical quantity.