Objectives Find lateral areas of cylinders Find surface areas of cylinders
Lateral Areas of Cylinders The axis of the cylinder is the segment with the endpoints that are centers of the circular bases. If the axis is also the altitude, then the cylinder is called a right cylinder. Otherwise, the cylinder is an oblique cylinder.
Tidbit of Knowledge The net of a cylinder is composed of two congruent circles and a rectangle. The area of this rectangle is the lateral area. The length of the rectangle is the same as the circumference of the base, 2 r 2 So, the lateral area of a right cylinder is 2 rh base
Example Find the lateral area of a right circular cylinder whose base has a radius of 4 inches and whose height is 6 inches. 4 6
6 4 Using the formula L=2 rh, we get… 2 x 3.14 x 6 x 4 equals 150.72 units 2
Surface Area If a right cylinder has a surface area of T units 2, a height of h units, and the bases have radii of r units, then T= 2 rh + 2 r 2. So basically, it’s the lateral area of the rectangle plus the area of the two bases (circles). Get it?
Example The diameter of the base of a cylinder is 12 cm and the height is 8 cm. Find the surface area of the solid cylinder. 8cm 12cm
Using T= 2 rh + 2 r 2 Plug it in: 2 x 3.14 x 6 x 8 + 2 x 3.14 x 6 2 Equals 301.44 + 226.08 So your answer should be... 527.5 cm 2