What is the relationship between the volume of a cylinder and the volume of a cone? Watch the following video to find out! http://www.youtube.com/watch?v=0ZACAU4SGyM

Since it takes three cones to fill one cylinder, i.e. 3 Vcone = 1 Vcylinder then to isolate a formula for volume of a cone: 3 Vcone = 1 Vcylinder 3 3 Vcone = 1 Vcylinder 3

What is the relationship between the volume of a cube and the volume of a square-based pyramid? Watch the following video to find out! http://www.youtube.com/watch?v=rTs9HwWiBaI

Since it takes three pyramids to fill one cube,                                                              Ad Since it takes three pyramids to fill one cube, i.e. 3 Vpyramid = 1 Vcube then to isolate a formula for volume of a pyramid: 3 Vpyramid = 1 Vcube 3 3 Vpyramid = 1 Vcube 3

In general, the volume of a cone or pyramid: where A is the area of the base and h is the height from apex to base. V = Ah 1 3 s a A square = Iength2 A circle = r2

Part C – Volume of Pyramids and Cones PYTHAGOREAN ALERT! [NB: slant height (s)  height of the pyramid (h)] a Example: A square-based pyramid has a slant height of 15 cm and apothem of 12 cm. Find the volume. Equation: Substitute: Solve: To find Asquare-base: A = (length)2 A = (2a)2 A = 4a2 A = 4(12)2 A = 576 To find height: h2 + a2 = s2 h2 + 122 = 152 h2 = 152 - 122 h2 = 225 – 144 h2 = 81 h = 9 (sqrt both sides) V = 1/3 Ah V = 1/3 (576) (9) V = 1728 h s=15 a a=12 a+a=2a  The volume of the pyramid is 1728 cm3