Answer
(a) See the explanation below.
(b) See the explanation below.
(c) See the explanation below.
Work Step by Step
a) A parametric surface, let us say $S$, is known to be a surface in $R^3$ with two parameters $(m,n)$ represented as:
$r(m,n)=p(m,n)i+q(m,n)j+r(m,n)k$
Here, $p,q,r$ are scalar functions.
The grid curves of a parametric surface $S$ are the curves that develop with keeping one of the parameters$(m,n)$ as constant.
b) Area of a surface parametric surface $S$ can be defined as: $\iint_D|r_m \times n_v|$ dA
where $(m,n) \in D$
c) Area of the surface $S$ of equation $z=g(x,y)$ can be calculated as:
$\iint_D\sqrt {1+(g_x)^2+(g_y)^2}dA=\iint_D\sqrt {1+(\dfrac{\partial z}{\partial x})^2+(\dfrac{\partial z}{\partial y})^2}dA$
