Surface Area of Cylinders
Surface area of cylinders is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume. The total surface area equals 2 pi r squared for the two circular bases plus 2 pi r h for the curved lateral surface. For a cylinder with radius 3 cm and height 8 cm, the surface area is 18 pi plus 48 pi equals 66 pi approximately 207.3 square centimeters.
Key Concepts
Property Cylinder with radius $r$ and height $h$: Surface Area $= 2\pi r^2 + 2\pi rh$ This consists of: Two circular bases: $2\pi r^2$ Curved lateral surface: $2\pi rh$.
Examples A cylinder with radius 3 cm and height 8 cm has a Surface Area of $2\pi(3^2) + 2\pi(3)(8) = 2\pi(9) + 2\pi(24) = 18\pi + 48\pi = 66\pi$ square cm, which is approximately $207.3$ square cm. A cylindrical can with radius 2 inches and height 5 inches has a Surface Area of $2\pi(2^2) + 2\pi(2)(5) = 8\pi + 20\pi = 28\pi$ square inches, which is approximately $87.9$ square inches. A cylinder with radius 4 ft and height 6 ft has a Surface Area of $2\pi(4^2) + 2\pi(4)(6) = 32\pi + 48\pi = 80\pi$ square ft, which is approximately $251.3$ square ft.
Explanation The surface area of a cylinder measures the total area of all its outside surfaces. This includes the two circular bases (top and bottom) plus the curved surface that wraps around the side. Think of it as the amount of material needed to completely cover the cylinder, like wrapping paper or paint.
Common Questions
What is the formula for the surface area of a cylinder?
Surface Area equals 2 pi r squared plus 2 pi r h, where r is the radius and h is the height. The first term is the area of the two circular bases and the second is the curved lateral surface.
How do you find the lateral surface area of a cylinder?
The lateral surface area is 2 pi r h, which represents the area of the curved side that wraps around the cylinder. Think of unrolling the side into a rectangle with width 2 pi r and height h.
What does the surface area formula for a cylinder represent?
The formula combines two circular base areas (2 pi r squared) with the curved side area (2 pi r h). Together these cover the entire outside surface of the cylinder.
What textbook covers cylinder surface area in Grade 7?
Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume covers the surface area formula for cylinders.