What is the surface area and volume of this shape?
Let us not mix the surfaces of a three dimensional figure with that of a simple two-dimensional plane. The surfaces of a three dimensional figure are the boundaries of the space that the figure occupies. These (plural) surfaces define the metrical structure or volume of the figure. A plane (singular area) defines only two dimensions. Thus if you are referring to the ends of a cylindrical figure, they should be circles and not squares. The volume of the figure would thus be the area of the circle multiplied by the height of the cylinder, and the surface area would be the area of the two circular ends plus the circumference of the circle multiplied by the height.
The vol. remains the same as that of cylinder as the square cannot hold anything. The surface area is the curved surface area of the cylinder +2*Area of the square+2*(Area of square-Area of the circle) The 3 parts of the surface area are the top of 2 squares the curved surface area of the cylinder and the third is the bottom of those squares. As the squares overlap the circle of the cylinder we subtract the area of the circle and thus get the area of the edges which are not overlapped by the circle of the cylinder.
