12.3 Surface Area of Circular Solids

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Presentation transcript:

12.3 Surface Area of Circular Solids cylinder cone sphere

Cylinder: base is a circle Contains 2 congruent parallel bases. Right circular cylinder perpendicular line from center to each base. Net: h r

Net: T113: LAcyl = Ch C = circumference h= height Lateral area: A = bh b = circumference (2πr or πd) h b h r

Total area: TA = 2(πr2) + 2πrh Lateral area: A = bh b = circumference (2πr or πd) Net: b h h r

Find the surface area of the following cylinder: 7cm TA = 2(πr2) + 2πrh 10cm

l Cone: base is a circle Slant height and lateral height are the same. l = slant height Cone will mean a right cone where the altitude passes through the center of the circular base.

l = slant height T114: LA = ½ Cl = πrl Net: C = circumference r = radius

Find the surface area of the cone. The diameter is 10 The slant height is 6 TA = LA + Abase = πr2 + πrl

Sphere: special surface area formula. NO lateral edges No lateral area Proof will come later – requires limits. Postulate: TA = 4πr2 Radius of the sphere!

Find the total surface area of the following shape Find the total surface area of the following shape. Hint: just what you see!