Cone

volume and surface area of cone, example question for cone

1. Cone and Frustrum of a Cone

2. What is a cone? A cone is a solid that has a circular base and a single vertex.

3. Types of Cones Right Cone-   Vertex is over the center of the base. Oblique Cone-   Vertex is not over the center of the base

4. Volume of Cone The volume of a cone is given by the formula: Where: r  is the radius of the circular base,   h  is the height - the perpendicular distance from the base to the vertex . Same for both right angle and oblique. Volume =

5. Example 1:

6. Example 2: The diagram below shows a conical container filled with water. The base of the cone lies on a horizontal table. The volume of water is 821 1/3 cm3. Using pi = 22/7, calculate the height , in cm, of the water in the container.

7. Surface Area of Cone The surface area of a cone is given by the formula Where: r is the radius of the circular base,   s  is the slant height of the cone. But there are no formulas for oblique cone.

8. Frustum of Cone A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). To find the slant height, we have to use The formula of the surface area is Area= without the area for both circles.

9. Frustum of Cone The formula for  frustum of a pyramid  or  frustum of a cone  is given by Where: h = perpendicular distance between A 1  and A 2  (h is called the altitude of the frustum) A 1  = area of the lower base A 2  = area of the upper base Note that A 1  and A 2  are parallel to each other.

10. Derivation http://www.mathalino.com/reviewer/derivation-of-formulas/derivation-of-formula-for-volume-of-a-frustum

11. Summary: Calculate the: 1) Volume of the cone. 2) Surface area of the cone. 3) Volume of the c onical frustrum . 4) Surface area of the conical frustrum . Height of water = 7