Such cones are called self dual cones We will see that the positive semide nite cone de ne it later which will be really important later is also a self dual cone Exercise 3 Show that is C D then D C 3 Dual cone of a closed and convex cone By the de nition of dual cone we know that the dual cone C is closed and convex Speci cally
E.g 4 A cone has base radius of cm and perpendicular height cm Find the exact surface area of the cone Express your answer in terms of r h r 2πr2 2πrh Surface area of a cylinder = 2πr2 2πrh Curved surface area of a cylinder = 2πrh Surface area of a sphere = 4πr2 6044 = πr2 πrl Surface area of a cone = πr2 πrl r l l r h r2 h2
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The volume of a cone is exactly one third the volume of a cylinder with the same radius and height The volume formula for a cylinder is V=Bh so to find the volume of a cone divide Bh by 3 area of the base shape height of the cone 6 Volume of ConesIn Class Notes Find the Volume of each coneRound to the nearest tenth 5in 12in .
If printed on 8x11 paper the cone template on this page will create a small cone and the template on the next page a medium cone for large cones use a copier to enlarge the template and print on bigger paper Step 2 Trace onto paper of choice and cut Step 3 Fold paper into cone Use bone folder and ruler to crease line where edges meet.
Height of cone Area of base EXAMPLE 1 Finding the Volume of a Cone Find the volume of the cone Round your answer to the nearest tenth The diameter is 4 meters So the radius is 2 meters V = 1 3 Bh Write formula for volume = 1 3 π 2 2 6 Substitute = 8π ≈ 25.1 Use a calculator The volume is about 25.1 cubic meters EXAMPLE 2
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Find the exact volume of each cone 10 An ice cream cone has a radius of 3 centimeter and a height of 9 centimeter Find the volume of the ice cream cone Volume = 1 Volume = 2 Volume = 3 Volume = 4 Volume = 5 Volume = 6 Volume = 7 Volume = 8 Volume = 9 Volume = 156 cm 33 m 30 in 343 m 150 ft 80 cm 204 ft 21 in 16 m 27 cm 4 cm 15 cm
