Geometry Surface Area and Volume of Spheres.

Size: px

Start display at page:

Download "Geometry Surface Area and Volume of Spheres."

Basil Bridges
5 years ago
Views:

1 Geometry 12.6 Surface Area and Volume of Spheres

2 11.7 Essential Question How do you find the surface area and volume of a sphere? Geometry 11.7 Surface Area and Volume of Spheres 2

3 Goals Find the surface area of spheres. Find the volume of spheres. Solve problems using area and volume. Geometry 11.7 Surface Area and Volume of Spheres

4 Sphere radius The set of points in space that are equidistant from the same point, the center. Great Circle (Divides the sphere into two halves.) Geometry 11.7 Surface Area and Volume of Spheres

5 Hemisphere Half of a sphere. r Geometry 11.7 Surface Area and Volume of Spheres 5

6 Sphere Formulas SA r 2 r V r Geometry 11.7 Surface Area and Volume of Spheres 6

7 Using a Calculator You may find it easier to use the formula for volume in this form: V = r π Geometry 11.7 Surface Area and Volume of Spheres 7

8 SA r 2 Example 1 Find the Surface Area and the Volume of a sphere with a radius of V r Geometry 11.7 Surface Area and Volume of Spheres 8

9 Your Turn Find the surface area and volume. SA in V Geometry 11.7 Surface Area and Volume of Spheres 9

10 Problem 1 A snowman is made with three spheres. The largest has a diameter of 2 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 11.7 Surface Area and Volume of Spheres 10

11 Problem 1 Solution A snowman is made with three spheres. The largest has a diameter of 2 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 11.7 Surface Area and Volume of Spheres 11

12 Problem 1 Solution The radii are 12 in, 10 in, and 8 in. V V V , cu in Geometry 11.7 Surface Area and Volume of Spheres 12

13 Or, for easier calculation V (8 ) (10 ) (12 ) ( ) (20) 1, Geometry 11.7 Surface Area and Volume of Spheres 1

14 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 11.7 Surface Area and Volume of Spheres 1

15 Problem 2 Solution Volume of Cylinder V = r 2 h V = (9 2 )(50) V = V = 050 V cu. ft. Geometry 11.7 Surface Area and Volume of Spheres 15

16 Problem 2 Solution Volume of Hemisphere V cu. ft. This is the volume of a sphere. The volume of the hemisphere is half of this value, which is cu. ft. Geometry 11.7 Surface Area and Volume of Spheres 16

17 Problem 2 Solution Volume of Cylinder Volume of Hemisphere Total Volume = cu. ft. Geometry 11.7 Surface Area and Volume of Spheres 17

18 Problem 2 Extension Total Volume =1250. cu. ft. One bushel contains 1.2 cubic feet. How many bushels are in the silo? = bushels Geometry 11.7 Surface Area and Volume of Spheres 18

19 Problem A sphere is inscribed inside a cube which measures 6 in. on a side. What is the ratio of the volume of the sphere to the volume of the cube? Geometry 11.7 Surface Area and Volume of Spheres 19

20 Problem Solution Volume of the Cube: = 216 cu in 6 Radius of the Sphere: 6 in. Volume of the Sphere: 6 V (27) 6 Geometry 11.7 Surface Area and Volume of Spheres 20

21 Problem Solution Volume of the Cube: 216 cu in Volume of the Sphere: 6 Ratio of Volume of Sphere to Volume of Cube Geometry 11.7 Surface Area and Volume of Spheres 21

22 Problem A mad scientist makes a potion in a full spherical flask which has a diameter of inches. To drink it, he pours it into a cup with a diameter of.5 inches and is.5 inches high. Will the potion fit into the cup? If not, how much is left in the flask? Geometry 11.7 Surface Area and Volume of Spheres 22

23 Problem Solution Flask Volume: Diameter = inches Radius = 2 inches V cu in Geometry 11.7 Surface Area and Volume of Spheres 2

24 Problem Solution.5 cu in Cup Volume: Diameter =.5 inches Radius = 1.75 inches Height =.5 inches V ( )(.5).7 cu in Geometry 11.7 Surface Area and Volume of Spheres 2

25 Problem Solution.5 cu in The flask holds.5 cu in..7 cu in The cup holds.7 cu in. Yes, the potion fits into the cup. Geometry 11.7 Surface Area and Volume of Spheres 25

26 Problem 5 The surface area of a sphere is 00 cm 2. Find: 1. Its radius, 2. The circumference of a great circle,. Its volume. Geometry 11.7 Surface Area and Volume of Spheres 26

27 Problem 5 Solutions SA r 2 C 2 r 00 r 2 r V 2 (.89) 0.72 r r 2.87 (. 89 ) r Geometry 11.7 Surface Area and Volume of Spheres 27

28 Last Problem On a far off planet, Zenu was examining his next target, Earth. The radius of the Earth is 96 miles. What is the volume of material that will be blown into space? Geometry 11.7 Surface Area and Volume of Spheres 28

29 Last Problem Solution V cubic miles 260,711,88,000 cu mi Geometry 11.7 Surface Area and Volume of Spheres 29

30 Summary A sphere is the set of points in space equidistant from a center. A hemisphere is half of a sphere. A great circle is the largest circle that can be drawn on a sphere. The diameter of a great circle equals the diameter of the sphere. Geometry 11.7 Surface Area and Volume of Spheres 0

31 Formulas to Know SA r 2 r V r Geometry 11.7 Surface Area and Volume of Spheres 1

32 Homework Page 762 Problems 10 17, all Geometry 11.7 Surface Area and Volume of Spheres 2

OML Sample Problems 2017 Meet 7 EVENT 2: Geometry Surface Areas & Volumes of Solids

OML Sample Problems 2017 Meet 7 EVENT 2: Geometry Surface Areas & Volumes of Solids Include: Ratios and proportions Forms of Answers Note: Find exact answers (i.e. simplest pi and/or radical form) Sample