Cylinders
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.
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 =
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
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