# Surface Area of Circular Solids Lesson 12.3 cone Surface Area of Circular Solids Lesson 12.3 cone cylinde r sphere Cylinder: Contains 2 congruent parallel bases that are circles. Right circular cylinder perpendicular

line from center to each base. h r Net : Theorem 113: h The lateral area of a cylinder is equal to

the product of the height and the circumference of the base. LAcyl = Ch = 2rhrhrh (C = circumference, h= height) r The total area of a cylinder is the sum of the cylinders lateral area and the areas of the two bases. T.A. = 2rhr2 + 2rhrh

Find the surface area following cylinder: 7cm (total) of the TA = 2rhrhr2rh + 2rhrhrh TA = 2rhrh(72rh) + 2rhrh(7)(10) 10cm

TA = 98 + 140rh + 140rh TA = 2rh38 + 140rh cm2rh l Cone: base is a circle Slant height and lateral height are the same. Cone will mean a right cone where the altitude passes through the center of the circular base.

Net: Theorem 114: The lateral area of a cone is equal to1/2rh the product of the slant height and the circumference of the base. LA = Cl = rhrl C = Circumference & l = slant height The total surface area of a cone is the sum of the lateral area and the area of the base. TA = rhr2rh + rhrl

Find the surface area of the cone. The diameter is 6 & the slant height is 8 + 140. TA = rhr2rh + rhrl = rh(3)2rh + rh3(8 + 140) = 9rh + 2rh4rh = 33rh units2rh Sphere: has NO lateral edges & No lateral

areaTA = 4rhr2rh Postulate: r = radius of the sphere Find the total area of the sphere: TA = 4rrr2 = 4rr52 = 100r units2 As a team, find the surface area of the following shape. Only find the area of the parts you can see.

16c m 17c m 10cm 1. Lateral area of a rhrl = rh8 + 140(17) = cone, 136rh

2rh. Plus the lateral area of the cylinder, 2rhrhrh = 2rhrh(8 + 140)(10) = 160rh 3. Plus the surface of the hemisphere. 4rhr2rh = (1/2rh)4rh(8 + 1402rh) = 12rh8 + 140rh 4. Add them up: 136rh + 160rh + 12rh8 + 140rh = 42rh4rh units2rh