Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find each volume to the nearest tenth. Use 3.14 for . 1. cylinder: radius = 6 m, height = 11 m 1,243.4 m3 2. rectangular prism: length = 10 cm, width = 8.64 cm, height = 12.9 cm 1,114.6 cm3 3. triangular prism: base area = 34 ft2, height = 18 ft 612 ft3 4. cylinder: diameter = 8 m, height = 18 m 904.3 m3

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

Sunshine State Standards MA.7.G.2.1 Justify and apply formulas for… volume of pyramids…and cones. Also MA.7.G.2.2

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.

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.

Additional Example 1A: Finding the Volume of a Rectangular Pyramid Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3 V = Bh Use the formula. 4 ft Find the area of the rectangular base. B = 5 · 7 = 35 1 3 V = · 35 · 4 Substitute for B and h. 7 ft 5 ft V ≈ 46.7 ft3 Multiply. 1 3 Estimate V = · 30 · 5 Round the measurements. V = 50 ft3 The answer is reasonable.

Additional Example 1B: Finding the Volume of a Rectangular Pyramid Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3 V = Bh Use the formula. Find the area of the triangular base. B = ½ · 30 · 25 = 375 1 3 V = · 375 · 26 Substitute for B and h. V = 3250 ft3 Multiply.

Check It Out: Example 1A Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

The answer is reasonable Check It Out: Example 1A 1 3 1 3 V = Bh = (8)(7)(4) V ≈ 74.7 about 74.7 ft3 Estimate. 1 3 V ≈ · 54 · 4 ≈ 72 The answer is reasonable

Check It Out: Example 1B Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Check It Out: Example 1B Continued 3 1 3 V = Bh B= (9)(19) = 85.5 1 3 V ≈ (85.5)(12) = 342 ≈ 342 m 2 Estimate. 1 3 V ≈ · 84 · 12 ≈ 336 The answer is reasonable

The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base.

Additional Example 2A: Finding the Volume of a Cone Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3 Use the formula. The base is a circle so B =  · r2  3.14 · 52  78.5. V = Bh 1 3 V  · 78.5 · 6 Substitute for B and h. V  157 yd3 Multiply. ·  ≈ 1. 1 3 V ≈ ·  52 · 6 1 3 Estimate  150 yd3 The answer is reasonable.

Additional Example 2B: Finding the Volume of a Cone Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3 Use the formula. The base is a circle so B =  · r2  3.14 · 32  28.26. V = Bh 7 cm 3 cm 1 3 V  · 28.26 · 7 Substitute for B and h. V  65.9 cm3 Multiply. ·  ≈ 1. 1 3 V ≈ ·  32 · 7 1 3 Estimate  63 cm3 The answer is reasonable.

The answer is reasonable. Check It Out: Example 2 Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. V = 1 3 V  29.31 about 29.3 cm3 Estimate: V ≈ ·  22 7  28 r2h  (3.14)(2)2(7) The answer is reasonable. 7 cm 4 cm

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 17 17

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. 1. 2. 80 ft3 301.4 yd3 3. 252 ft3

Lesson Quiz for Student Response Systems 1. Identify the volume of the prism. A. 576 ft3 B. 288 ft3 C. 96 ft3 D. 24 ft3 19 19

Lesson Quiz for Student Response Systems 2. Identify the volume of cone to the nearest tenth. Use 3.14 for . A. 4240.0 in3 B. 3815.1 in3 C. 1271.7 in3 D. 141.3 in3 20 20

Lesson Quiz for Student Response Systems 3. Identify the volume of the pyramid. A. 1632 ft3 B. 544 ft3 C. 192 ft3 D. 27 ft3 21 21