9-2D Surface Area and Volume of Spheres

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9-2D Surface Area and Volume of Spheres

• How many bases does a sphere have?
• What measurement do you need to know in a sphere?
• What is the formula for the surface area of a
  sphere?
• What is the formula for the volume of a sphere?

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How many bases..

• Does a prism have?
• Does a pyramid have?
• Does a cylinder have?
• Does a cone have?
• Does a sphere have?

2 1 2 1 0
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Sphere Measuring

• What one measurement do you need to know when
  working with a sphere?
• The center?
• The diameter?
• The radius?

No ? yes
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Theorem

• The surface area of a sphere is 4p times the
  square of its radius.
• SA 4 p r2

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Find the Surface Area of the Sphere

• SA 4p r2
• SA 4p(5)2
• SA 100p (exact)
• SA 314.2 (approx)

r 5
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Theorem

• The volume of a sphere is four-thirds the product
  of p and the cube of its radius.
• V 4/3 p r 3

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Find the Volume of the Sphere

• V 4/3 p r 3
• V 4/3 p (5) 3
• V 166?p (exact)
• V 523.6 (approx)

r 5
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Find the Volume and the Surface Area of a sphere

• When the area of one its great circles is 4p.
• What do circle area and sphere volume/surface
  area have in common?
• Radius!!!

A 4p
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Find the Volume and the Surface Area of a sphere

• A pr2
• 4p pr2
• r2 4
• r 2
• V 4/3 p r 3
• V 4/3 p (2) 3
• V 10?p
• V 33.5

A 4p
SA 4pr2 SA 4p(2)2 SA 16p SA 50.3
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Find the volume of a sphere whose surface area is
36p
SA 36p

• SA 4 p r2
• 36p 4p r2
• 9 r2
• r 3

V 4/3 p r 3 V 4/3 p (3)3 V 36p V 113.1
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Tennis Anyone?

• A cylindrical can of tennis spheres contains
  three balls. The radius of each ball is about
  3.25 cm.
• Find the dimensions of the can.
• Find the volume of the can.
• Find the volume of the tennis balls.

H 19.5,r 3.25 V 647.07 V 431.38
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• How many bases does a sphere have?
• 0
• What measurement do you need to know in a sphere?
• radius
• What is the formula for the surface area of a
  sphere?
• SA 4 p r2
• What is the formula for the volume of a sphere?
• V 4/3 p r 3

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Assignment 9-2D

• Page 641, 1-6, 19-22

No Formulas with numbers No Credit