Find the volume of the solid. Problem of the Day

Section 12-6 Surface Areas and Volumes of Spheres

Then Now Objectives You found the surface areas of prisms and cylinders. Find surfaces areas of spheres. Find volumes of spheres.

Common Core State Standards Content Standards G.GMD.1 – Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. G.GMD.3 – Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Mathematical Practices 1) Make sense of problems and persevere in solving them. 6) Attend to precision. Common Core State Standards

Vocabulary

Find the surface area of each sphere. Example 1

Find the surface area of each hemisphere. Example 1

Great Circle: the circle that contains the center of a sphere Great Circle: the circle that contains the center of a sphere. Poles: the endpoints of a diameter of a great circle. Vocabulary

Example 2 Find the surface area of each sphere or hemisphere. sphere: circumference of great circle = π cm hemisphere: area of great circle ≈ 4π f t 2 Example 2

Find the volume of each sphere. Example 3

Find the volume of each hemisphere. Example 3

Find the surface area and volume of the sphere and hemisphere. Examples 1 & 3

Ren inflates a spherical balloon to a circumference of about 14 inches Ren inflates a spherical balloon to a circumference of about 14 inches. He then adds more air to the balloon until the circumference is about 18 inches. What volume of air was added to the balloon? Example 4

p.884 #10 – 13, 18, 19, 29, 53, 55 Homework

Marcus builds a sphere inside of a cube Marcus builds a sphere inside of a cube. The sphere fits snugly inside the cube so that the sphere touches the cube at one point on each side. The side length of the cube is 2 inches. What is the volume of the remaining space inside the cube? Problem of the Day