1. PRE-ALGEBRA

2. 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)

3. 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). 1313 1313 1313

4. PRE-ALGEBRA Find the volume of the cone. V = Bh Use the formula for volume. 1313 V = (  r 2 )h B =  r 2 1313 = 16   16 (3.14)  50.24 The volume of the cone is 16  in. 3, or about 50 in. 3. 1313 =  (2) 2 (12) Replace r with 2 and h with 12. Simplify. LESSON 10-9 Additional Examples Volume: Pyramids Cones and Spheres

5. 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.) 1313 1313 1313

6. 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. 1313 V = (s 2 )h B = s 2 (Substitute) 1313 = (8) 2 (12) Replace s with 8 and h with 12. 1313 = 256 Simplify. LESSON 10-9 Additional Examples Volume: Pyramids Cones and Spheres

7. 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)  14.13 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.) 4343 4343 4343

8. 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. 4343 260,579,713,159 = 82,987,169,796  4343 =  (3,963) 3 Replace r with 3,963. Simplify. LESSON 10-9 Additional Examples Volume: Pyramids Cones and Spheres

9. 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 2 864 m 3 LESSON 10-9 Volume: Pyramids Cones and Spheres Lesson Quiz