10.6: Volumes of Pyramids and Cones Objective: To find the volume of pyramids and cones.

Volume: The space that a figure occupies. Volume of a Pyramid: FORMULA: H V = 1/3 BH

Volume of a Cone: FORMULA: V = 1/3 BH or V = 1/3  r²H H

Example 1: Find the volume of a square pyramid with base edges 15 cm & height 22cm. V = 1/3 BH = 1/3s 2 H = 1/3 (15) 2 (22) = 1650 cm³

Example 2: Find volume of a square pyramid with base edges 16 m and a slant height 17 m: What is missing? How do we find it? H Pythagorean Theorem

Now, find volume V = 1/3 BH = 1/3bhH = 1/3(16)(16)(15) = 1/3(16)(16)(15) = 1280 m³ = 1280 m³ Find H Find H 17² = 8² + H² 289 = 64 + H² 225 = H² 15 = H 15 = H H

Ex. #3 You try: Find the volume of a square pyramid with base edges 24 m and slant height 13 m: V = 1/3 BH = 1/3s 2 H = 1/3(24) 2 (5) = 1/3(24) 2 (5) = 960 m³ = 960 m³ Find H ( ) 5 = H 5 = H

Example 4: Find the volume of the oblique cone: V = 1/3  r²H = 1/3  (3²)(11) = 1/3  (3²)(11) = 33  in³ = 33  in³

Ex. 5 You try: Find the volume of each cone in terms of  and also rounded as indicated: a. To the nearest m 3 V = 1/3  r²H = 1/3  (6²)(12) = 144  m³ = 144  m³ ≈ 452 m³ ≈ 452 m³

b. To the nearest mm 3. V = 1/3  r²H = 1/3  (21²)(42) = 6174  mm³ = 6174  mm³ ≈ mm³ ≈ mm³

Assignment: Pg 554 #2-14 even, 15-18, 22-23, 28