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Spheres

Spheres. Information. Volume and surface area of a sphere. A sphere is a 3D shape with a surface the same distance from the center at every point. This fixed distance is the radius of the sphere. A sphere is generated by rotating a circle, or half circle, around an axis. r. 4. 2 3. 4 3.

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Spheres

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  1. Spheres

  2. Information

  3. Volume and surface area of a sphere A sphere is a 3D shape with a surface the same distance from the center at every point. This fixed distance is the radius of the sphere. A sphere is generated by rotating a circle, or half circle, around an axis. r

  4. 4 2 3 4 3 2 3 3 Volume of a sphere The volume of a sphere can be described in terms of the volume of a cylinder. The volume of a sphere is the volume of a cylinder with the same radius and with a height of 2r. Use this information to derive the formula for the volume of a sphere. πr2h volume of a cylinder: sphere volume πr2(2r) substitute height of cylinder: = πr3 2πr3 distribute: πr3 multiply by :

  5. 4 3 Surface area of a sphere For a sphere with a radius of r the surface area is: sphere surface area = 4πr2 Find the surface area and volume of a sphere with a radius of 4cm, to the nearest hundredth. find surface area: SA = 4π(4)2 4cm = 201.06cm2 find volume: V = π(4)3 = 268.08cm3

  6. 4 4 3 3 Surface Area The earth is not perfectly spherical, but it is very close. The radius of the earth is approximately 3,963.2 miles. What is the approximate volume of the earth? use the formula for volume of a sphere: V = πr3 V = π(3,963.2)3 V = 260,751,356,862 cubic miles What is the surface area of the earth? use the formula for surface area of a sphere: V = 4π(3,963.2)2 V = 197,379,408.2 square miles About 71% of the earth’s surface is water. What area is water? What area is land?

  7. Crystal ball

  8. 4 3 Cross-sections No matter which way you take a cross-section of a sphere it will always be circular. A cross-section of a sphere that passes through the center of the sphere will have the same radius as the sphere. A cross-section of a sphere has a radius of 6.6cm. What is the volume of the sphere? What is the surface area? volume = π(6.6)3 = 1204.3cm3 surface area = 4 π(6.6)2 = 547.4cm2

  9. Summary

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