1. 10-5: Surface Area of Pyramid and Cone
Page 710
17)
V = 1107π m3
18)
V = 16π/3 in3
19)
V = 144π ft3
20)
Volume is 1/27
22)
V = 240π ft3
24)
V = 21π in2
25)
V = 25π/6 m3
26)
V = 11760π ft3
27)
V = 240π cm3
33)
C = 10π√3 cm
36)
S = 600π yd2
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10-5: Surface Area of Pyramid and Cone

2. 10-5: Surface Area of Pyramid and Cone
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10-5: Surface Area of Pyramid and Cone

3. 10-5: Surface Area of Pyramid and Cone
Fiesta
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10-5: Surface Area of Pyramid and Cone

4. Section 10-6 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us
Spheres
Section 10-6
Geometry PreAP, Revised ©2014
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10-5: Surface Area of Pyramid and Cone

5. 10-5: Surface Area of Pyramid and Cone
Spheres
A sphere is the locus of points in space that are a fixed distance from a given point.
A radius of a sphere connects the center of the sphere to any point on the sphere.
A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres
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10-5: Surface Area of Pyramid and Cone

6. Volume Formulas for Cylinders
Surface Area of a Sphere: SA = 4πr2
Volume of a Sphere: V = (4/3)πr3 where r is the radius
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10-5: Surface Area of Pyramid and Cone

7. 10-5: Surface Area of Pyramid and Cone
Archimedes Tomb
Archimedes was the first to discover that the volume of a sphere is 2/3 the volume of the cylinder that circumscribes it. He considered this to be his greatest mathematical achievement.
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10-5: Surface Area of Pyramid and Cone

8. 10-5: Surface Area of Pyramid and Cone
Why… Let’s Derive
h = 2r
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10-5: Surface Area of Pyramid and Cone

9. 10-5: Surface Area of Pyramid and Cone
Example 1
Find the volume of the sphere. Give your answer in terms of .
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10-5: Surface Area of Pyramid and Cone

10. 10-5: Surface Area of Pyramid and Cone
Example 2
If the volume of a sphere is 972 m3, what is the radius?
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10-5: Surface Area of Pyramid and Cone

11. 10-5: Surface Area of Pyramid and Cone
Your Turn
Find the diameter of a sphere with volume 36,000 cm3.
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10-5: Surface Area of Pyramid and Cone

12. 10-5: Surface Area of Pyramid and Cone
Example 3
Find the volume of the hemisphere.
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10-5: Surface Area of Pyramid and Cone

13. 10-5: Surface Area of Pyramid and Cone
Example 4
Find the volume of the composite figure.
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10-5: Surface Area of Pyramid and Cone

14. 10-5: Surface Area of Pyramid and Cone
Your Turn
Find the volume of the composite figure.
V = 45 – 18 = 27 ft3
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10-5: Surface Area of Pyramid and Cone

15. Investigation
Think of a sphere as being constructed by a whole bunch of pyramids. The height of each pyramid would be the radius of the sphere. B
n = a whole bunch
h = radius of the sphere

16. Investigation
Let’s also say that each of these pyramids is congruent and has a base area of B. Thus, the surface area of the sphere is: B

17. Investigation
Furthermore, the volume of the sphere should be the sum of the volumes of the pyramids. B

18. Investigation
Use the two formulas below to derive a formula for the surface area of a sphere. B
4r2 ≈ nB

19. 10-5: Surface Area of Pyramid and Cone
Example 5
Find the surface area of a sphere with diameter 76 cm. Give your answers in terms of .
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10-5: Surface Area of Pyramid and Cone

20. 10-5: Surface Area of Pyramid and Cone
Example 6
Find the volume of a sphere with surface area 324 in2. Give your answers in terms of .
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10-5: Surface Area of Pyramid and Cone

21. 10-5: Surface Area of Pyramid and Cone
Your Turn
What is the difference between the volume and surface area of this hemisphere below?
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10-5: Surface Area of Pyramid and Cone

22. 10-5: Surface Area of Pyramid and Cone
Assignment
Page all, all, 25, 26
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10-5: Surface Area of Pyramid and Cone