7.6: Surface Area and Volume of a Sphere

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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.

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What will we learn today?
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Sphere

• Defn A sphere is the set of all points in space
  at a certain distance (_________) from a certain
  point (__________).

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Volume of a Sphere

• Let V be the volume of a sphere with radius r.
• Then V ____________.

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• 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?

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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.
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Surface Area of a Sphere
The volume of each pyramid is ?Bhpyr ?Br.
Lets assume there are n pyramids in the sphere.
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Surface Area of a Sphere
So the volume of the sphere is 1/3B1r 1/3B2r
1/3Bnr 1/3r(B1B2Bn).
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Surface Area of a Sphere
The sum of the pyramids base areas is the
surface area of the sphere. So Vsphere 4/3pr3
?Sr, where S is the surface area of the sphere.
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Surface Area of a Sphere

• Solve the equation below to derive the formula
  for the surface area of a sphere.
• Vsphere 4/3pr3 ?Sr

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Surface Area of a Sphere

• Let S be the surface area of a sphere with radius
  r. Then S

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• A childs ball is 12 inches in diameter. Ignoring
  thickness, how much material was needed to make
  the ball?

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• A clay sphere has volume 36p cm3. If someone cuts
  straight through the sphere, the cross section is
  a circle. What is the area of the largest
  circular cross section?
• 48 p cm2
• 36 p cm2
• 9 p cm2
• 6 p cm2
• 4 p cm2

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Assignment

• pages 474-475,
• 10-30 (multiples of 5), 32, 33, 37-42 (all).