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Exploring Volume: Pyramids, Cones, Spheres

Understand and calculate volumes of pyramids, cones, and spheres with examples and real-world scenarios.

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Exploring Volume: Pyramids, Cones, Spheres

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  1. Lesson Menu Main Idea and New Vocabulary Key Concept: Volume of a Pyramid Example 1: Find the Volume of a Pyramid Example 2: Real-World Example Key Concept: Volume of a Cone Example 3: Find the Volume of a Cone Key Concept: Volume of a Sphere Example 4: Find the Volume of a Sphere

  2. Find the volumes of pyramids, cones, and spheres. • sphere Main Idea/Vocabulary

  3. Key Concept

  4. Volume of a pyramid B = 7 ● 3, h = 20 Simplify. Find the Volume of a Pyramid Find the volume of the pyramid. Round to the nearest tenth, if necessary. Answer: The volume is about 140 cubic centimeters. Example 1

  5. Find the volume of the pyramid. Round to the nearest tenth, if necessary. A. 200 ft3 B. 300 ft3 C. 400 ft3 D. 600 ft3 Example 1 CYP

  6. Volume of a pyramid Replace V with 9 and B with 3 • 3 or 9. AWARD The Amazing Bread Company gives a pyramid-shaped award to students who have learned how to use the food pyramid to choose from the 5 food groups. The award has a square base with sides 3 inches long. If the volume is 9 cubic inches, find the height of the award. 9 = 3hMultiply. Example 2

  7. Divide each side by 3. 3 = hSimplify. Answer: The height is 3 inches. Example 2

  8. PAPERWEIGHT A pyramid-shaped paperweight has a rectangular base with sides 8 centimeters and 11 centimeters long. If the volume is 176 cubic inches, find the height of the paperweight. A. 2 cm B. 4 cm C. 6 cm D. 8cm Example 2 CYP

  9. Key Concept 2

  10. Volume of a cone Replace r with 1.5 and h with 8. Simplify. Use a calculator. Find the Volume of a Cone Find the volume of the cone. Round to the nearest tenth. Since the diameter is 3 meters, the radius is 1.5 meters. Answer: The volume is about 18.8 cubic meters. Example 3

  11. Find the volume of the cone. Round to the nearest tenth. A. 138.2 mm3 B. 414.7 mm3 C. 622.0 mm3 D. 1,244.1 mm3 Example 3 CYP

  12. Key Concept 4

  13. r3 Volume of a sphere ●  ● 73 Replace r with 7. Simplify. Use a calculator. Find the Volume of a Sphere Find the volume of the sphere. Round to the nearest tenth. Answer: The volume of the sphere is about 1,436.8 cubic centimeters. Example 4

  14. Find the volume of the sphere. Round to the nearest tenth. A. 37.3 ft3 B. 339.3 ft3 C. 2,290.2 ft3 D. 3,053.6 ft3 Example 4 CYP

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