343 pi in^3 ; exact volume
1078 in^3 ; Approximate volume
Since it's not specified, I will assume the axis of rotation will be one edge of the square. With that in mind, here's the solution.
Since the shape specified is a square with an area of 49 in^2, the length of any edge will be sqrt(49) = 7 inches.
Since we're rotating along one edge, we will create a cylinder with a radius of 7 inches and a height of 7 inches. The volume will be the area of a circle with a 7 inch radius multiplied by the height of the cylinder. So
V = pi*h*r^2
V = pi*7*7^2
V = pi*7*49
V = pi*343
V = 343pi
V = 1077.56628; approximately.
So the exact volume is 343pi in^3 and an approximate volume is 1078 in^3
