This isn't rocket science, it's rocket math!Geometry Level 3
In this above rocket picture,
- The top black line serves as the height of the cone portion of the rocket and the bottom black line serves as the height of the "lamp shade" portion of the rocket. Both black lines have a length of 5 inches.
- The red line serves as the height of the cylindrical portion of the rocket and has a length of 10 inches.
- The green line serves as the radius of the cone portion and cylindrical portion. The green line also serves as the smaller radius of the lampshade portion. The length of the green line is 1 inch.
The blue line serves as the larger radius of the lampshade portion, and has a length of 2 inches.
If the surface area of the rocket (in square inches) equals \( SA \), find \( \left \lfloor SA \right \rfloor \).
Note: This "rocket" has a sealed base. Please include the base in your answer.