PRE-ALGEBRA

How do you find volume of a cone or a pyramid? Volume of a Pyramid or Cone Formula Volume. ( pyramid or cone ) =  B  h where B is the area of the Base and h is the height (not slant height) Proof: The volume of a pyramid is one third of the volume of a prism with the same base and height. In other words, if you fill the three pyramids below with sand and pour the sand into a prism with the same height and base, you will fill the prism to the top. This is also true with a cone and a cylinder with the same radius and height (it will take exactly three cones full of sand to fill the cylinder) Volume: Pyramids, Cones, and Spheres (10-9) 1313 Therefore, the volume of a pyramid is 1/3 · area of base (B) · height (h)

PRE-ALGEBRA Volume: Pyramids, Cones, and Spheres (10-9) Example: Find the volume of the following cone. V = BhVolume formula for a cone =  r 2 hB =  r 2 (Substitute.) =  (3) 2 (10) r = 3, h = 10 (Substitute.) = 30   30 (3.14)  94 ft. 3 (cubic feet) The volume of the cone is about 94 ft 3 (In other words, about 94 cubes that measure one foot on each side will fit inside it)

PRE-ALGEBRA Find the volume of the cone. V = Bh Use the formula for volume V = (  r 2 )h B =  r = 16   16 (3.14)  The volume of the cone is 16  in. 3, or about 50 in =  (2) 2 (12) Replace r with 2 and h with 12. Simplify. LESSON 10-9 Additional Examples Volume: Pyramids Cones and Spheres

PRE-ALGEBRA Volume: Pyramids, Cones, and Spheres (10-9) Example: Find the volume of the following cone. V = BhVolume formula for a pyramid = s 2 hB = s 2 (one side squares) =  (6) 2 (10) s = 6, h = 10 (Substitute.) = 120 The volume of the cone is 120 ft 3. (In other words, exactly 120 cubes that measure one foot on each side will fit inside it.)

PRE-ALGEBRA Find the volume of the square pyramid. The volume of the pyramid is 256 in. 3. V = Bh Use the formula for volume V = (s 2 )h B = s 2 (Substitute) 1313 = (8) 2 (12) Replace s with 8 and h with = 256 Simplify. LESSON 10-9 Additional Examples Volume: Pyramids Cones and Spheres

PRE-ALGEBRA How do you find volume of a sphere? Volume of a Sphere Formula Volume. ( sphere ) =    r 3 where r is the radius of the sphere. Volume: Pyramids, Cones, and Spheres (10-9) 4343 Example: Find the volume of the following of the bottom sphere of the snow statue. V =  r 3 Volume formula for a sphere =  (1.5) 3 r = ½d = ½(3) = 1.5 (Substitute.)  (3.14)(3.375) .  3.14  4.5 (3.14)  The volume of the cone is 14 ft 3. (In other words, exactly 14 cubes that measure one foot on each side will fit inside it.)

PRE-ALGEBRA Earth has an average radius of 3,963 mi. What is Earth’s approximate volume to the nearest 1,000,000 mi 3 ? Assume that Earth is a sphere. The volume of the Earth is about 260,580,000,000 mi 3. V =  r 3 Use the volume formula ,579,713,159 = 82,987,169,796  4343 =  (3,963) 3 Replace r with 3,963. Simplify. LESSON 10-9 Additional Examples Volume: Pyramids Cones and Spheres

PRE-ALGEBRA Find the volume of each space figure to the nearest unit. 1.a cone with diameter 9 cm and height 12 cm 2.a square pyramid with base edges 12 m and height 18 m 3.a basketball with diameter 10 in. about 523 in. 3 about 254 cm m 3 LESSON 10-9 Volume: Pyramids Cones and Spheres Lesson Quiz