Consider the solid G in the first octant bounded above by z = 2 − x^2 − y^2 , below by z = 0, laterally by y = 0, and x = 0, and x^2 + y^2 = 1. (a) Sketch G accurately. (b) Sketch the base R...

Consider the solid G in the first octant bounded above by z = 2 − x^2 − y^2
, below
by z = 0, laterally by y = 0, and x = 0, and x^2 + y^2 = 1.
(a) Sketch G accurately.
(b) Sketch the base R accurately.
(c) Set up an integral to find the area of the cap S using appropriate theorems.
(d) Evaluate the integral to find the area of the cap S exactly