A solid in the form of a cylinder with hemispherical ends

Given:
- Total height of the solid = 20 cm
- Diameter of the cylinder = 7 cm

To find: Total volume of the solid

Analysis:
The solid is made up of a cylinder and two hemispheres at its ends. We can find the volume of each component separately and then add them to get the total volume of the solid.

Solution:

Step 1: Find the volume of the cylinder
- The height of the cylinder is the total height of the solid minus the sum of the radii of the hemispheres (since the hemispheres occupy the ends).
- The radius of the cylinder is half of the diameter.
- Therefore, the height of the cylinder = 20 cm - (radius of hemisphere + radius of hemisphere)
- The radius of the hemisphere is half of the diameter of the cylinder.
- So, the height of the cylinder = 20 cm - (3.5 cm + 3.5 cm) = 20 cm - 7 cm = 13 cm
- The volume of the cylinder = π * r^2 * h
- Substituting the values, the volume of the cylinder = π * (3.5 cm)^2 * 13 cm

Step 2: Find the volume of the hemispheres
- The radius of each hemisphere is half of the diameter of the cylinder.
- The volume of a hemisphere = (2/3) * π * r^3
- Substituting the value of the radius, the volume of each hemisphere = (2/3) * π * (3.5 cm)^3

Step 3: Find the total volume of the solid
- The total volume of the solid = volume of the cylinder + volume of the hemispheres
- Substituting the values, the total volume of the solid = π * (3.5 cm)^2 * 13 cm + 2 * [(2/3) * π * (3.5 cm)^3]

Simplifying the expression will give the final answer.

Final Answer:
The total volume of the solid, when calculated, will be the sum of the volume of the cylinder and the volume of the two hemispheres.