A prism is a 3-D object where the end faces are 2 parallel congruent polygons. A cylinder is a prism where the end faces are circles.

Volume (V) is the amount of space a three-dimensional (3-D) figure occupies. Volume is expressed in cubed units such as mm³, yd³, or ft³. The volume formula for cylinders is Volume = Area of the circle base × Height.

Surface area (S) is the sum of the areas of all the faces, or surfaces, of a three-dimensional (3-D) figure. Surface area is expressed in squared units such as m², cm², or mi². The surface area formula for cylinders is Surface area = Area of the side + Area of the circle ends.

The easiest way to understand surface area is to think of a cylinder as a can. If you want to cover the can with paper, the surface area is how much paper you need to cover the entire can: top, bottom, and side. The side of the can is like the label. When flattened, the label of a can is actually a rectangle. The area of a rectangle is base × height. In this case, the base is the circumference of the circle and the height is the height of the can. So the area of the rectangle is 2 π r × height. The area of the top is π r². Since the top and bottom are the same size, multiply the area formula by 2 to get the area of both top and bottom.

h = height r = radius   Volume = Area of the circle base × height V = π radius 2 × height   = π r 2 × h Surface area = Area of the side + Area of the circle ends S = (2 π radius)(height) + 2 π radius 2   = (2 π r)(h) + 2 π r 2   = 2 π r h + 2 π r 2

Example 1:

Find the surface area and volume. Answer with proper units. To represent m², use sq m. To answer with π, use 'pi'. Sample area: 5pi sq m. Sample volume: 5pi cu m

Surface Area = Volume =

S = 2 π r h + 2 π r 2   = 2 π (2 in)(5 in) + 2 π (2 in)2   = 20 π in 2 + 2 π (4 in2)   = 20 π in 2 + 8 π in2   = 28 π in 2

V = π r 2 × h   = π (2 in) 2 × 5 in   = π (4 in 2) × 5 in   = 20 π in 3

The answer is Surface Area =   Volume =