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# Cones

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### Cones

1. 1. Start
2. 2. Whatare Cones? • A cone is an n- dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex. More
3. 3. A cone is said to be right when the vertex is directly above the centre of the base. When the vertex of a cone is not vertically above the center of the base, it is called an oblique cone.
4. 4. Nets The net of a cone consists of the following two parts: •a circle that gives the base; and •a sector that gives the curved surface Examples of Cones
5. 5. Formulas 1. VOLUME r : radius h : height (the perpendicular distance from the base to the apex). Example: Calculate the volume of a cone if the height is 12 cm and the radius is 7 cm. Solution: Volume
6. 6. 2. SURFACE AREA Surface area of cone = Area of sector + area of circle Solution: Area = πr(r + s) = = 1,257.14 cm2 Example: A cone has a circular base of radius 10 cm and a slant height of 30 cm. Calculate the surface area.
7. 7. Word Problems 1. The radius of a right cone is 3 cm and its surface area is 24∏ cm2. Find the height and volume of this cone. Solution: Start with the equation for surface area since the radius is given as 3 cm and the surface area as 24∏. S = 24p S = ∏ r2 + ∏ rs S = ∏ 32 + ∏ 3s S = 3 ∏(3 + s) Solving this equation for s we get 24 ∏= 3 ∏(3 + s) 8 = 3 + s s = 5 cm Next
8. 8. To calculate the volume we need to find the values of h. Since h, r, and s form a right triangle, we can use the Pythagorean Theorem to calculate the value of h. h2 + r2 = s2 h2 + 32 = 52 h2 = 25 - 9 h2 = 16 h = 4 cm Now use r = 3 cm and h = 4 cm in the formula for volume: Answer: Height = 4 cm Volume = 12∏ cm3
9. 9. 2. The radius of a cone is 5 inches and the volume is 100∏ cubic inches. Find the slant height and surface area of this cone. Solution: Using the formula for the volume of a cone and the fact that r = 5 in: Solve the equation for h: h = 12 in Next
10. 10. Use r = 5 and h = 12 in the Pythagorean Theorem to find the value for the slant height s. h2 + r2 = s2 122 + 52= s2 144 + 25 = s2 s2 = 169 s = 13 inches Use r = 5 and s = 13 in the formula for surface area: S = ∏ r 2 + ∏ rs S = ∏ 52 + ∏ (5)(13) S = ∏ (25 + 65) S = 90 ∏ square inches Answer: Slant height = 13 inches Surface Area = 90 ∏ square inches
11. 11. The End Group Names: • Stephanie • Mikky • Sonia • Wivan • Alvin • Jessica