Surface Areas & Volume of Cylinders Tutorial 9a

Lateral and Surface Area §A cylinder has two congruent parallel bases. §The bases of a cylinder are circles. §An altitude of a cylinder is a perpendicular segment that joins the planes of the bases. §The height h of a cylinder is the length of an altitude. Right cylinders Oblique cylinder h h h bases

Lateral and Surface Area Theorem §The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder. L.A. = Ch or 2  rh §The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases. S.A. = L.A. + 2B = 2  rh + 2  r 2 h r B is the area of a base

Lateral and Surface Area §To find the lateral area of a cylinder, unroll it and the area of the rectangle formed is the lateral area. §The surface area of a cylinder is the sum of the lateral area and the areas of the two circular bases. h r Lateral Area Surface Area h 2  r r r Area of base B =  r 2 L.A. = 2  rh S.A = L.A. +2B = 2  rh+2  r 2

1. 2. S.A = L.A. +2B = 2  rh+2  r 2  2(3.14)517+2(3.14)(5) 2   ft 2 Find the surface area of each cylinder to the nearest tenth. S.A = L.A. +2B = 2  rh+2  r 2  2(3.14)320+2(3.14)(3) 2   ft 2 h = r = 5 h = r =

Volume of a Cylinder §The volume of a cylinder is the product of the area of a base and the height of the cylinder. r h B