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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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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

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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

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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.

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

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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.

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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.

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

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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.

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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?

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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

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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.

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Ex. 3: Finding the Surface Area of a Sphere

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Volume of a Sphere radius C

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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:

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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

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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

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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^.=

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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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