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Comparing Volumes: Earth vs. Soccer Ball

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nora-white
10 diapositives · 279 Views · Nov 07, 2014

In this lesson, students will explore the concept of volume by comparing the volume of the Earth to that of a soccer ball. They will learn how to calculate the volume of spheres using the formula ( V = frac{4}{3} pi r^3 ). The lesson will include practical exercises, such as finding the volume of spheres with differing radii and understanding the properties of spherical shapes. By the end, students will grasp how volume can vary greatly between large and small spheres and apply their knowledge to real-world examples.

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  1. Spheres 6-10 Course 3 Essential Question How does the volume of the earth compare to the volume of a soccer ball? Learn to find the volume of spheres. Objective 8.G.9

  2. Spheres 6-10 Course 3 Vocabulary A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphereis agreat circle.

  3. Spheres 6-10 Course 3 The volume of a hemisphere is exactly halfway between the volume of a cone and a cylinder with the same radius r and height equal to r.

  4. Spheres 6-10 Course 3

  5. Spheres 6-10 4 3 V = pr3 = p(9)3 4 3 Course 3 Additional Example 1: Finding the Volume of a Sphere Find the volume of a sphere with radius 9 cm, both in terms of p and to the nearest tenth of a unit. Volume of a sphere Substitute 9 for r. = 972p cm3 3,052.1 cm3

  6. Spheres 6-10 4 3 V = pr3 = p(3)3 4 3 Course 3 Try This: Example 1 Find the volume of a sphere with radius 3 m, both in terms of p and to the nearest tenth of a unit. Volume of a sphere Substitute 3 for r. = 36p cm3 113.0 m3

  7. Spheres 6-10 Course 3 Insert Lesson Title Here Lesson Quiz: Part 1 Find the volume of each sphere, both in terms of  and to the nearest tenth. Use 3.14 for p. 1.r = 4 ft 2.d = 6 m 85.3p ft3, 267.8 ft3 36p m3, 113.0 m3

  8. Spheres 6-10 Course 3 Insert Lesson Title Here Lesson Quiz: Part 2 5.A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume? 412 in3 United Streaming video clip – Defining properties of 3-D figures – Discovering Math: Geometry Grades 6-8

  9. Spheres 6-10 Course 3 Insert Lesson Title Here Chapter 6 Summary of Formulas 6-1 A=bh for area of a rectangle & parallelogram 6-2 A=1/2bh for area of a triangle 6-3 A=1/2h(b1+b2) for area of a trapezoid 6-4 C= d or C=2r for the circumference of a circle 6-6 V=Bh or V = r2h for volume of a cylinder Note: Capital B stands for the area of the base!

  10. Spheres 6-10 Course 3 Insert Lesson Title Here Chapter 6 Summary of Formulas con’t 6-7 V=1/3Bh or V=1/3r2h for the volume of a cone 6-10 V=(4/3)r3 for the volume of a sphere and S=4r2 for the surface area of a sphere KNOW ALL OF THESE FORMULAS…. YOU WILL BE TESTED ON THEM FROM NOW TO MAY!