Final answer:
To find the area of the resulting surface when a curve is rotated about the y-axis, we can use the formula for the surface area of revolution.
Step-by-step explanation:
To find the area of the resulting surface when the given curve is rotated about the y-axis, we can use the formula for the surface area of revolution. The formula is given by:
A = 2π∫ab(y√(1+(dy/dx)²))dx
In this case, the curve is represented by the equation y = x³/², and the limits of integration are a = 5 and b = 21. We can plug these values into the formula and calculate the area.