8-9 Volume of Pyramids and Cones Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

8-9 Volume of Pyramids and Cones Warm Up Find each volume to the nearest tenth. Use 3.14 for . 1. cylinder: radius = 6 m, height = 11 m 1,243.4 m 3 1,114.6 cm ft m 3 2. rectangular prism: length = 10 cm, width = 8.64 cm, height = 12.9 cm 3. triangular prism: base area = 34 ft 2, height = 18 ft 4. cylinder: diameter = 8 m, height = 18 m

8-9 Volume of Pyramids and Cones Problem of the Day When my age is divided by 2, 3, 4, or 6 there is always a remainder of 1, but when it is divided by 7 there is no remainder. How old am I? 49

8-9 Volume of Pyramids and Cones MA.7.G.2.1 Justify and apply formulas for… volume of pyramids…and cones. Also MA.7.G.2.2 Sunshine State Standards

8-9 Volume of Pyramids and Cones Suppose you have a square-pyramid-shaped container and a square-prism-shaped container, and the bases and heights are the same size. If you pour sand from the pyramid into the prism, it appears that the prism holds three times as much sand as the pyramid.

8-9 Volume of Pyramids and Cones In fact, the volume of a pyramid is exactly one- third the volume of a prism with the same height and a congruent base. The height of a pyramid is the perpendicular distance from the pyramid’s base to the vertex opposite the base.

8-9 Volume of Pyramids and Cones Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Additional Example 1A: Finding the Volume of a Rectangular Pyramid V = 1313 Bh Use the formula. B = 5 · 7 = 35 Find the area of the rectangular base. V = 1313 · 35 · 4 Substitute for B and h. V ≈ 46.7 ft 3 Estimate 5 ft 7 ft 4 ft Multiply. V = 1313 · 30 · 5 Round the measurements. V = 50 ft 3 The answer is reasonable.

8-9 Volume of Pyramids and Cones Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Additional Example 1B: Finding the Volume of a Rectangular Pyramid V = 1313 Bh Use the formula. B = ½ · 30 · 25 = 375 Find the area of the triangular base. V = 1313 · 375 · 26 Substitute for B and h. V = 3250 ft 3 Multiply.

8-9 Volume of Pyramids and Cones Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Check It Out: Example 1A

8-9 Volume of Pyramids and Cones Check It Out: Example 1A V = 1313 Bh V ≈ 74.7 Estimate. V ≈ 1313 · 54 · 4 ≈ = (8)(7)(4) about 74.7 ft 3 The answer is reasonable

8-9 Volume of Pyramids and Cones Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Check It Out: Example 1B

8-9 Volume of Pyramids and Cones Check It Out: Example 1B Continued V = 1313 Bh Estimate. V ≈ 1313 · 84 · 12 ≈ B= (9)(19) = 85.5 ≈ 342 m The answer is reasonable 1313 (85.5)(12) = 342 V ≈ 2

8-9 Volume of Pyramids and Cones The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base.

8-9 Volume of Pyramids and Cones Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. Additional Example 2A: Finding the Volume of a Cone V = 1313 Bh V  1313 · 78.5 · 6 V  157 yd 3 Estimate Use the formula. The base is a circle so B =  · r 2  3.14 · 5 2  Substitute for B and h. Multiply ·  ≈ V ≈ ·  5 2 · 6  150 yd 3 The answer is reasonable.

8-9 Volume of Pyramids and Cones Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. Additional Example 2B: Finding the Volume of a Cone V = 1313 Bh V  1313 · · 7 V  65.9 cm 3 Estimate Use the formula. The base is a circle so B =  · r 2  3.14 · 3 2  Substitute for B and h. Multiply ·  ≈ V ≈ ·  3 2 · 7  63 cm 3 The answer is reasonable. 7 cm 3 cm

8-9 Volume of Pyramids and Cones Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. Check It Out: Example 2 7 cm 4 cm V = 1313 V  about 29.3 cm 3 Estimate: 1313 V ≈ ·   28  r 2 h (3.14)(2) 2 (7) 1313 The answer is reasonable.

8-9 Volume of Pyramids and Cones Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

8-9 Volume of Pyramids and Cones Lesson Quiz Find the volume of each pyramid or cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable ft yd ft 3

8-9 Volume of Pyramids and Cones 1. Identify the volume of the prism. A. 576 ft 3 B. 288 ft 3 C. 96 ft 3 D. 24 ft 3 Lesson Quiz for Student Response Systems

8-9 Volume of Pyramids and Cones 2. Identify the volume of cone to the nearest tenth. Use 3.14 for . A in 3 B in 3 C in 3 D in 3 Lesson Quiz for Student Response Systems

8-9 Volume of Pyramids and Cones 3. Identify the volume of the pyramid. A ft 3 B. 544 ft 3 C. 192 ft 3 D. 27 ft 3 Lesson Quiz for Student Response Systems