Final answer:
To find the area of the surface that lies inside the given plane and cylinder, we need to determine the region of overlap between them.
Step-by-step explanation:
To find the area of the surface that lies inside the given plane and cylinder, we need to determine the region of overlap between them.
The equation of the plane is 4x + 5y + z = 20, and the equation of the cylinder is x^2 + y^2 = 25. By substituting the first equation into the second one, we can find the intersection curve of the plane and the cylinder. Once we have the intersection curve, we can use it to find the desired area by integrating over the region.
Since this is a complex calculation, it is recommended to use appropriate mathematical software or consult a teacher or tutor for step-by-step assistance.