Chapter 16: Surface Area and Volume 223A cylinder is a solid with two circles as parallel bases
and a rectangle wrapped around to join them.Surface Area
The surface area of a cylinder is the total of the areas of the two circles at the ends, plus the area
of the rectangle that forms the sides. (Think about a label on a can. If you remove it from the can
and unroll it, it’s a rectangle.) The area of each circle is Sr^2. The rectangle has a height equal
to the height of the cylinder and a base equal to the circumference of the circle, so its area is
circumference v h or 2Srh. The total surface area is SA = Sr^2 + 2Srh.
Suppose that a can is going to be made in the shape of a cylinder with a radius of 4 inches and a
height of 10 inches. How much metal will be needed to make the can? The metal needed to make
the can is the surface area of the cylinder. Each of the two circular bases has an area of 16S. The
curved surface of the can unrolls to a rectangle whose base is the circumference of the circle, 8S,
and whose height is 10. The total surface area is 2 v 16 S + 8S v 10 = 32S + 80S = 112S square
inches. That’s approximately 351.8 square inches.Volume
The similarities between prisms and cylinders hold up when volume is concerned. The volume
of a prism is the area of the base times the height, and the volume of a cylinder is the area of its
base, a circle, times its height. That makes the volume formula V = Sr^2 h.
To find the volume of the cylinder whose diameter and height are both 4 inches, first find the
radius. If the diameter = 4 inches, the radius = 2 inches, so the area of the base = 4S square
inches. The volume is the area of the base times the height, or 4S·4=16S cubic inches. That’s
approximately 50.24 cubic inches.