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Surface Area and Volume of Spheres A sphere is the set of all points in space that are the same distance from a point, the center of the sphere.

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Presentation on theme: "Surface Area and Volume of Spheres A sphere is the set of all points in space that are the same distance from a point, the center of the sphere."— Presentation transcript:

1 Surface Area and Volume of Spheres A sphere is the set of all points in space that are the same distance from a point, the center of the sphere.

2 A radius of a sphere is a segment from the center to a point on the sphere. A chord of a sphere is a segment whose endpoints are on the sphere. Surface Area and Volume of Spheres

3 A diameter is a chord that contains the center. As with all circles, the terms radius and diameter also represent distances, and the diameter is twice the radius. Surface Area and Volume of Spheres

4 More... If a plane intersects a sphere, the intersection is either a single point or a circle. If the plane contains the center of the sphere, then the intersection is a great circle of the sphere. Every great circle of a sphere separates a sphere into two congruent halves called hemispheres.

5 Surface Area of a Sphere Surface area = 4 π (radius) 2 S = 4 π r 2 C Radius

6 Find the Surface Area of a Sphere Find the surface area of the sphere. Round your answer to the nearest whole number. The radius is 8 in. 8 in.

7 Find the Surface Area of a Sphere Find the surface area of the sphere. Round your answer to the nearest whole number. The radius is 5 cm. 10 cm.

8 Ex. 1: Comparing Surface Areas Find the surface area. When the radius doubles, does the surface area double?

9 S = 4  r 2 = 4  2 2 = 16  in. 2 S = 4  r 2 = 4  4 2 = 64  in. 2 The surface area of the sphere in part (b) is four times greater than the surface area of the sphere in part (a) because 16  4 = 64  So, when the radius of a sphere doubles, the surface area DOES NOT double.

10 Ex. 2: Using a Great Circle The circumference of a sphere (also referred to as the circumference of the great circle) is 13.8  feet. What is the surface area of the sphere?

11 Solution: Begin by finding the radius of the sphere. C = 2  r 13.8  = 2  r 13.8  = r (To solve for r, divide both sides by 2  ) 2  6.9 = r

12 Solution: Using a radius of 6.9 feet, the surface area is: S = 4  r 2 = 4  (6.9) 2 = 190.44  ft. 2 So, the surface area of the sphere is 190.44  feet squared.

13 Ex. 3: Finding the Surface Area of a Sphere

14 Volume of a Sphere radius C

15 Find the Volume of a Sphere Find the volume of the sphere. Round your answer to the nearest whole number. a. 2 ft. 4Ab/c32^3 = Using your calculator, input:

16 Find the Volume of a Sphere Find the volume of the hemisphere. Round your answer to the nearest whole number. Note: A hemisphere has HALF the volume of a sphere. So simply use the volume formula, then ½ the answer. a 5 in. Using your calculator, input: 4Ab/c35^3= ≈ 523.95877 /2= ≈ 262

17 Find the Volume of a Sphere Find the volume of the sphere. Write your answer in terms of. 6 in. Be sure to remember to include when you write your answer  4Ab/c36^ 3 = To leave your answer in terms of pi… simply don’t input 288x

18 Last Example: Find r, if V = 2  V = 4  r 3 3 2  = 4  r 3 3 6  = 4  r 3 1.5 = r 3 1.14  r Formula for volume of a sphere. Substitute 2  for V. Multiply each side by 3. Divide each side by 4 . Use a calculator to take the cube root. 32nd15^.=

19 The End Assignment: 6.9 NTG p. 245 – 251 all VOCABULARY on p. 245 –Sketch picture or write definition. NOTES PAGES p. 246-248 – Read and fill in the blanks. PRACTICE p. 249-251 – Complete 1 – 33 all. If you get stuck, refer back to your Presentation Notes.


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