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Exploring Volumes of Pyramids and Cones for Maths Enthusiasts

Dive into calculating the volumes of pyramids and cones with engaging examples, real-world applications, and TEKS concepts.

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Exploring Volumes of Pyramids and Cones for Maths Enthusiasts

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  1. LESSON 12–5 Volumes of Pyramids and Cones

  2. Five-Minute Check (over Lesson 12–4) TEKS Then/Now Key Concept: Volume of a Pyramid Example 1: Volume of a Pyramid Key Concept: Volume of a Cone Example 2: Volume of a Cone Example 3: Real-World Example: Find Real-World Volumes Concept Summary: Volumes of Solids Lesson Menu

  3. Find the volume of the prism. Round to the nearest tenth if necessary. A. 240 in3 B. 200 in3 C. 120 in3 D. 100 in3 5-Minute Check 1

  4. Find the volume of the cylinder. Round to the nearest tenth if necessary. A. 785.4 cm3 B. 547.3 cm3 C. 314.2 cm3 D. 157.1 cm3 5-Minute Check 2

  5. What is the volume of the cylinder. Round to the nearest tenth if necessary. A. 627.5 m3 B. 843.4 m3 C. 986.4 m3 D. 1017.9 m3 5-Minute Check 3

  6. What is the volume of the prism? Round to the nearest tenth if necessary. A. 225.4 ft3 B. 203.7 ft3 C. 183.8 ft3 D. 152.8 ft3 5-Minute Check 4

  7. Find the volume of a rectangular prism with a length of 12 yards, a width of 14 yards, and a height of 9 yards. A. 1110 yd3 B. 1227 yd3 C. 1512 yd3 D. 2012 yd3 5-Minute Check 5

  8. The volume of a triangular prism is 655 cubic feet. The height of the prism is 5 feet. Find the area of one triangular base. A. 65.5 ft2 B. 131 ft2 C. 650 ft2 D. 660 ft2 5-Minute Check 6

  9. Targeted TEKS G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. G.11(D) Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. Mathematical Processes G.1(D), G.1(E) TEKS

  10. You found surface areas of pyramids and cones. • Find volumes of pyramids. • Find volumes of cones. Then/Now

  11. Concept

  12. s 3, h 7 21 Volume of a Pyramid Find the volume of the square pyramid. Volume of a pyramid Multiply. Answer: The volume of the pyramid is 21 cubic inches. Example 1

  13. A.416 ft3 B. C. D. Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid. Example 1

  14. Concept

  15. Volume of a Cone A. Find the volume of the oblique cone to the nearest tenth. Example 2A

  16. Volume of a Cone Volume of a cone r = 9.1, h = 25 ≈ 2168.0 Use a calculator. Answer: The volume of the cone is approximately 2168.0 cubic feet. Example 2A

  17. Volume of a Cone B. Find the volume of the cone to the nearest tenth. Example 2B

  18. Volume of a Cone Volume of a cone r = 5, h = 12 ≈ 314.2 Use a calculator. Answer: The volume of the cone is approximately 314.2 cubic inches. Example 2B

  19. A. Find the volume of the oblique cone to the nearest tenth. A. 444.4 m3 B. 27,463.2 m3 C. 3051.5 m3 D. 9154.4 m3 Example 2A

  20. B. Find the volume of the cone to the nearest tenth. A. 3015.9 m3 B. 125.7 m3 C. 1005.3 m3 D. 251.3 m3 Example 2B

  21. Find Real-World Volumes SCULPTUREAt the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth. Volume of a pyramid B = 36 ● 36, h = 52.5 Simplify. Answer: The volume of the pyramidion is 22,680 cubic centimeters. Example 3

  22. SCULPTUREIn a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth. A. 18,775 cm3 B. 19,500 cm3 C. 20,050 cm3 D. 21,000 cm3 Example 3

  23. Concept

  24. LESSON 12–5 Volumes of Pyramids and Cones

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