Final answer:
The lateral surface area of the right circular cone generated by revolving the region bounded by the given lines around the y-axis is 156π square units.
Step-by-step explanation:
To find the lateral surface area of the right circular cone generated by revolving the region bounded by y = 5x/12, y = 5, and x = 0 about the y-axis, we first need to understand the shape and dimensions of this cone.
The line y = 5x/12 represents the slope of the cone's side when revolved around the y-axis, forming the slant height of the cone. Since the region is also bounded by y = 5, this value represents the height (h) of the cone. The x-value at y = 5 can be found by rearranging the equation of the line to x = 12y/5, and substituting y = 5 gives us x = 12. Hence, the radius (r) of the cone's base is 12 units.
The Pythagorean theorem tells us that the slant height (l) of the cone can be found by solving the right triangle with sides of 5 (height) and 12 (radius), which gives us l = 13. The formula for lateral surface area (A) of the cone is A = πrl, where r is the radius and l is the slant height. Substituting the known values, we get A = π(12)(13), which simplifies to A = 156π square units.