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Answer :
The given parametric equations define a portion of a sphere of radius 3 centered at the origin.
To see this, notice that the x, y, and z coordinates are given in terms of spherical coordinates with radius r=3. Specifically,
x = 3cos(u)sin(v) = rcos(u)sin(v)
y = 3sin(u)sin(v) = rsin(u)sin(v)
z = 3cos(v) = rcos(v)
where r = 3 is the fixed radius of the sphere.
The limits of the parameters u and v determine the portion of the sphere that is being described. The range 0 ≤ u ≤ 1.57 (or π/2 in radians) corresponds to a quarter of the sphere, specifically the part of the sphere in the first and second quadrants where x is positive. The range 0 ≤ v ≤ 1.57 corresponds to the upper half of the sphere, where z is positive.
In summary, the given equations describe a quarter of a sphere of radius 3 centered at the origin, in the first and second quadrants where x is positive, and in the upper hemisphere where z is positive.
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