1. Surface Area & Volume of Spheres Objective: 1) To find the surface area & volume of a sphere.

2. Spheres Sphere – The set of all points in space equidistant from a given point. Center r Radius – Is a segment that has one endpt @ the center & the other endpt on the sphere. Diameter – A segment passing through the center w/ both endpts on the sphere.

3. Great Circles Great Circle – A cross-section of a sphere that also contains the center of the sphere. –Circumference of the G. Circle = Circumference of the sphere. –A G. Circle divides the sphere into 2 hemisphere. –Any cross section (G. Circle) of the sphere is a circle.

4. Surface Area of a sphere r SA = 4  r 2 Radius of a sphere

5. Ex.1: SA of a sphere Find the surface area of a sphere w/ a diameter of 8m. SA = 4  r 2 = 4  (4) 2 = 4  (16) = 64  = 201.1m 2 4m

6. Ex.2: Circumference and SA The circumference of the Earth is 24,902miles. Find the Surface Area of the Earth. SA = 4  r 2 = 4  (3963) 2 = 197,387,018 miles 2 C = 2  r 24,902 = 2  r r = 3963 miles

7. Volume of a sphere V s = (4/3)  r 3 Radius of a sphere r

8. Ex.3: Find the volume of the following sphere. 30m V s = (4/3)  r 3 = (4/3)  (15) 3 = (4/3)  (3375) = 4500  = 14137m 3

9. Ex.4: SA & Volume The surface area of a sphere is 125in 2. Find its volume to the nearest whole number. SA = 4  r 2 125 = 4  r 2 r = 3.2in V s = (4/3)  r 3 = (4/3)  (3.2) 3 = (4/3)  (31.4) = 43.7  = 137in 3

10. What have we learned?? V s = (4/3)  r 3 Radius of a sphere r SA = 4  r 2