1. Geometry 8.3 Volume of Spheres
Topic/Objective: To find the volume of a sphere.
EQ: How can you determine the volume of a sphere when given the radius of the sphere?

2. Geometry 8.3 Volume of Spheres
The set of points in space that are equidistant from the same point, the center.
radius
Geometry 8.3 Volume of Spheres

3. Geometry 8.3 Volume of Spheres
Hemisphere
Half of a sphere. r
Geometry 8.3 Volume of Spheres

4. Geometry 8.3 Volume of Spheres
Sphere Formulas r
Geometry 8.3 Volume of Spheres

5. Geometry 8.3 Volume of Spheres
Using a Calculator
You may find it easier to use the formula for volume in this form:
Geometry 8.3 Volume of Spheres

6. Geometry 8.3 Volume of Spheres
Example
Find the Volume of a sphere with a radius of 2. 2
Geometry 8.3 Volume of Spheres

7. Your Turn Find the volume.
Geometry 8.3 Volume of Spheres

8. Geometry 8.3 Volume of Spheres
Problem 1
A snowman is made with three spheres. The largest has a diameter of 24 inches, the next largest has a diameter of 20 inches, and the smallest has a diameter of 16 inches. Find the volume of the snowman.
Geometry 8.3 Volume of Spheres

9. Geometry 8.3 Volume of Spheres
Problem 1 Solution
A snowman is made with three spheres. The largest has a diameter of 24 inches, the next largest has a diameter of 20 inches, and the smallest has a diameter of 16 inches. Find the volume of the snowman.
The radii are 12 in, 10 in, and 8 in.
Geometry 8.3 Volume of Spheres

10. Geometry 8.3 Volume of Spheres
Problem 1 Solution
The radii are 12 in, 10 in, and 8 in.
13, cu in
Geometry 8.3 Volume of Spheres

11. Geometry 8.3 Volume of Spheres
Problem 2
This is a grain silo, as found on many farms. They are used to store feed grain and other materials. They are usually cylindrical with a hemispherical top.
Assume that the concrete part has a height of 50 feet, and the diameter of the cylinder is 18 feet.
Find the volume of the silo.
Geometry 8.3 Volume of Spheres

12. Geometry 8.3 Volume of Spheres
Problem 2 Solution
Volume of Cylinder
V = r2h
V = (92)(50)
V =   81  50
V = 4050
V  cu. ft. 18 50 9
Geometry 8.3 Volume of Spheres

13. Geometry 8.3 Volume of Spheres
Problem 2 Solution
Volume of Hemisphere 18 50 9
This is the volume of a sphere. The volume of the hemisphere is half of this value, which is cu. ft.
Geometry 8.3 Volume of Spheres

14. Geometry 8.3 Volume of Spheres
Problem 2 Solution
Volume of Cylinder
Volume of Hemisphere
1526.8
Total Volume
= cu. ft. 18 50 9
Geometry 8.3 Volume of Spheres

15. Geometry 8.3 Volume of Spheres
Problem 2 Extension
Total Volume = cu. ft.
One bushel contains cubic feet. How many bushels are in the silo?
 =
bushels
Geometry 8.3 Volume of Spheres

16. Geometry 8.3 Volume of Spheres
Problem 4
A mad scientist makes a potion
in a full spherical flask which has a diameter of 4 inches. To drink it, he pours it into a cylindrical cup with a diameter of 3.5 inches and is 3.5 inches high. Will the potion fit into the cup? If not, how much is left in the flask?
Skip
Geometry 8.3 Volume of Spheres

17. Geometry 8.3 Volume of Spheres
Problem 4 Solution
Flask Volume:
Diameter = 4 inches
Radius = 2 inches
Geometry 8.3 Volume of Spheres

18. Geometry 8.3 Volume of Spheres
Problem 4 Solution
33.5 cu in
Cup Volume:
Diameter = 3.5 inches
Radius = 1.75 inches
Height = 3.5 inches
Geometry 8.3 Volume of Spheres

19. Geometry 8.3 Volume of Spheres
Problem 4 Solution
33.5 cu in
33.7 cu in
The flask holds 33.5 cu in.
The cup holds 33.7 cu in.
Yes, the potion fits into the cup.
Geometry 8.3 Volume of Spheres

20. Geometry 8.3 Volume of Spheres
Last Problem
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On a far off planet, Zenu was examining his next target, Earth. The radius of the Earth is 3963 miles. What is the volume of material that will be blown into space?
Geometry 8.3 Volume of Spheres

21. Geometry 8.3 Volume of Spheres
Last Problem Solution
Geometry 8.3 Volume of Spheres