1. 11/21/20157.6: Surface Area and Volume of Spheres 7.6: Surface Area and Volume of a Sphere Expectation: G1.8.1: Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

2. What will we learn today? 11/21/20157.6: Surface Area and Volume of Spheres

3. 11/21/20157.6: Surface Area and Volume of Spheres Sphere Defn: A sphere is the set of all points in space at a certain distance (_________) from a certain point (__________).

4. 11/21/20157.6: Surface Area and Volume of Spheres Volume of a Sphere Let V be the volume of a sphere with radius r. Then V= ____________.

5. 11/21/20157.6: Surface Area and Volume of Spheres A scoop of ice cream is 2 inches in diameter. An ice cream cone is 2 inches in diameter and has a height of 3.5 inches. If the ice cream melted before any of it was eaten, would it all fit in the cone?

6. 11/21/20157.6: Surface Area and Volume of Spheres Surface Area of a Sphere If the sphere were filled with pyramids, then the sum of the volumes of the pyramids would be the volume of the sphere.

7. 11/21/20157.6: Surface Area and Volume of Spheres Surface Area of a Sphere The volume of each pyramid is ⅓Bh pyr = ⅓Br. Let’s assume there are n pyramids in the sphere.

8. 11/21/20157.6: Surface Area and Volume of Spheres Surface Area of a Sphere So the volume of the sphere is 1 / 3 B 1 r + 1 / 3 B 2 r + …+ 1 / 3 B n r =1 / 3 r(B 1 +B 2 +…+B n ).

9. 11/21/20157.6: Surface Area and Volume of Spheres Surface Area of a Sphere The sum of the pyramids’ base areas is the surface area of the sphere. So V sphere = 4 / 3 πr 3 = ⅓Sr, where S is the surface area of the sphere.

10. 11/21/20157.6: Surface Area and Volume of Spheres Surface Area of a Sphere Solve the equation below to derive the formula for the surface area of a sphere. V sphere = 4 / 3 πr 3 = ⅓Sr

11. 11/21/20157.6: Surface Area and Volume of Spheres Surface Area of a Sphere Let S be the surface area of a sphere with radius r. Then S =

12. 11/21/20157.6: Surface Area and Volume of Spheres A child’s ball is 12 inches in diameter. Ignoring thickness, how much material was needed to make the ball?

13. A clay sphere has volume 36π cm 3. If someone cuts straight through the sphere, the cross section is a circle. What is the area of the largest circular cross section? A. 48 π cm 2 B. 36 π cm 2 C. 9 π cm 2 D. 6 π cm 2 E. 4 π cm 2 11/21/20157.6: Surface Area and Volume of Spheres

14. 11/21/20157.6: Surface Area and Volume of Spheres Assignment pages 474-475, #10-30 (multiples of 5), 32, 33, 37-42 (all).