10.2.5 Spheres Key Objectives
• Learn and apply the formula for the volume of a sphere. • Learn and apply the formula for the surface area of a sphere. Key Terms • A sphere is the locus of points in space that are a fixed distance from a given point called the center of the sphere . • A radius of a sphere connects the center of the sphere to any point on the sphere. • A hemisphere is half of a sphere. • A great circle divides a sphere into two hemispheres. Formulas • Volume of a Sphere The volume of a sphere with radius r is V πr . 3 = • Surface Area of a Sphere The surface area of a sphere with radius r is S = 4 πr 2 . Example 1 Finding Volumes of Spheres 4 3
The volume of a sphere is determined in this example. The radius of the sphere is given. To obtain the volume, substitute the radius length into the formula for the volume of a sphere. The volume is 288 π cm 3 .
The diameter of a sphere is determined in this example. The volume of the sphere is given. To obtain the diameter, substitute the volume into the formula for the volume of a sphere. Solve for the radius and multiply by 2 to obtain the diameter. The diameter is 24 in.
211
Made with FlippingBook - PDF hosting