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Spheres

Spheres. Unit 13, Lesson 7. Spheres. The radius of the sphere is the distance from the center to the points on the sphere. Of all shapes, a sphere has the smallest surface area for its volume. Spheres.

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Spheres

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  1. Spheres Unit 13, Lesson 7

  2. Spheres • The radius of the sphere is the distance from the center to the points on the sphere. • Of all shapes, a sphere has the smallest surface area for its volume.

  3. Spheres • A great circle is the largest circle that can be drawn on a sphere.  Such a circle will be found when the cross-sectional plane passes through the center of the sphere.

  4. Spheres • A hemisphere is the half sphere formed by a plane intersecting the center of a sphere.

  5. Spheres • The surface area of a sphere is four times the area of the largest cross-sectional circle (called the great circle). SA = 4πr2 • Note:  A cross section of a geometric solid is the intersection of a plane and the solid.

  6. Spheres • The volume of a sphere is four-thirds times pi times the radius cubed.

  7. Example 1 The radius of this sphere is 4 feet. Find the area of the great circle of this sphere to the nearest tenth. • 12.7 sq ft • 50.3 sq ft • 804.2 sq ft

  8. Example 2 At the age of 81, Mr. Luke Roberts decided to start collecting string.  He has a spherical ball of string three feet in diameter.  On the assumption that one cubic inch of string weighs 0.03 pounds and the ball was solid string, how much does the ball weigh to the nearest tenth of a pound? • 73.0 lbs • 583.2 lbs • 732.9 lbs • 2442.9 lbs

  9. Example 3 When you blow up a balloon it forms a sphere because it is trying to hold as much air as possible with as small a surface as possible. How much air, to the nearest tenth of a cubic inch, is being held by a spherical balloon with a diameter of 12 inches? • 150.8 cu.in. • 226.2 cu.in. • 904.8 cu.in. • 7238.2 cu.in.

  10. Example 4 A cylinder and a sphere have the same radius and the same height.  What is the ratio of the volume of the cylinder to the volume of the sphere? • 1:1 • 2:1 • π:3 • 3:2

  11. Example 5 At the MetroPlex movie theater, popcorn is served in a box.  At the CinemaPlex movie theater, popcorn is served in a cylindrical container.  At home, Mom serves popcorn in a bowl (hemisphere in shape).  Based upon the given dimensions, where are you getting the most popcorn?(Disregard the thickness of the container.)

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