A parametric curve is defined by x = cos(πt/2), y = sin(πt/2) in the range of 0 ≤ t ≤ 1. It is rotated about the X axis by 360°. What is the area of the…

Explanation

For 0 ≤ t ≤ 1 the point (cos πt/2, sin πt/2) traces a quarter of the unit circle from (1, 0) to (0, 1). Rotating it about the X axis gives a hemisphere of radius 1, whose curved surface area is 2πr² = 2π.