1. 10.6 Surface Area & Volume of Spheres

2. Warm up
1. List three spheres you would see in real life. 2. Find the area of a circle with a 6 cm radius. 3. Find the volume of a cylinder with the circle from #2 as the base and a height of 5 cm. 4. Find the volume of a cone with the circle from #2 as the base and a height of 5 cm.

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

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

6. Surface Area of a sphere
SA = 4r2 r
Radius of a sphere

7. Ex.1: SA of a sphere
Find the surface area of a sphere w/ a diameter of 8m.
SA = 4r2
= 4(4)2
= 4(16)
= 64
= 201.1m2 4m

8. Ex.2: Circumference and SA
The circumference of the Earth is 24,902miles. Find the Surface Area of the Earth.
SA = 4r2
= 4(3963)2
= 197,387,018 miles2
C = 2r
24,902 = 2r
r = 3963 miles

9. Example 3: Find the surface area of the figure below.
SA sphere = 4πr²
Hemisphere is half but you also have a base.
SA = ½(4π6²)+ B =72π + B
B = πr² = π6² = 36π
SA = 72π + 36π
= 108π cm² ≈ cm²

10. Volume of a sphere
Vs = (4/3)r3 r
Radius of a sphere

11. Ex.4: Find the volume of the following sphere.
Vs = (4/3)r3
= (4/3)(15)3
= (4/3)(3375)
= 4500
= 14137m3
30m

12. Ex.5: SA & Volume
The surface area of a sphere is 125in2. Find its volume to the nearest whole number.
Vs = (4/3)r3
= (4/3)(3.2)3
= (4/3)(31.4)
= 43.7
= 137in3
SA = 4r2
125 = 4r2
r = 3.2in

13. What have we learned??
Vs = (4/3)r3 r
Radius of a sphere
SA = 4r2