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?

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

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

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

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

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

Your Turn Find the volume. Geometry 8.3 Volume of Spheres

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

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

Geometry 8.3 Volume of Spheres Problem 1 Solution The radii are 12 in, 10 in, and 8 in. 13,571.68 cu in Geometry 8.3 Volume of Spheres

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

Geometry 8.3 Volume of Spheres Problem 2 Solution Volume of Cylinder V = r2h V = (92)(50) V =   81  50 V = 4050 V  12723.5 cu. ft. 18 50 9 Geometry 8.3 Volume of Spheres

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 1526.8 cu. ft. Geometry 8.3 Volume of Spheres

Geometry 8.3 Volume of Spheres Problem 2 Solution Volume of Cylinder 12723.5 Volume of Hemisphere 1526.8 Total Volume 12723.5 + 1526.8 = 14250.3 cu. ft. 18 50 9 Geometry 8.3 Volume of Spheres

Geometry 8.3 Volume of Spheres Problem 2 Extension Total Volume =14250.3 cu. ft. One bushel contains 1.244 cubic feet. How many bushels are in the silo? 14250.3  1.244 = 11455.2 bushels Geometry 8.3 Volume of Spheres

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

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

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

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

Geometry 8.3 Volume of Spheres Last Problem Skip 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

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