VOLUME OF SPHERES

EOG Warm up: Tuesday, March 3 2015 1. Write the linear equation passing through points (13, 10) and (10, 16). 2. Find y given x = 7. 4x – 2y = 12 3. The volume of cube shaped box is 64 in³. What is the side length? Find x. 5. Find x. x2 +10 = 46 6. What is the side length of a square if the area is 121cm²? x 13 12

We’ll start the lesson today by reviewing yesterday’s lesson on volume of cylinders and cones. You will need your chrome books. Log in to Kahoot.it. Use the code given. When I say go, you may begin. Let’s see who has it! 

What do you know about spheres What do you know about spheres? Let’s see if you can fill in some of the blocks below. Work as a group. Definition: Formula: SPHERES Non-Examples: Examples:

Copy the following down on your piece of paper Copy the following down on your piece of paper. This will become part of your notes. Definition: Formula: A sphere is a 3D shape where every point on the surface is the same distance from the center. V = SPHERES Examples: Non-Examples: Basketball Planets (Earth) Dodgeball Orange Eyeball Bubble Circle Pizza Egg Drum Football

Watch this video to find out. Let’s look at how the volume of the sphere relates to the volume of the cylinder. Can you predict how many times a sphere will fill a cylinder with the same diameter and height? Actual: Watch this video to find out. http://www.teachertube.com/video/deriving-the-formula-volume-of-sphere-273985

In your groups, try and see if you can come up with the formula for volume of a sphere. I’ll give you about 5 minutes. Use what you learned from the video and your knowledge of cylinders. Here is a clue: A sphere fills a cylinder twice, so the volume of a sphere is 𝟐 𝟑 the volume of a cylinder (V = 𝝅 𝒓 𝟐 h). What is the difference in the shapes?

Volume of a sphere = 𝟐 𝟑 the volume of a cylinder: V = 𝟐 𝟑 x 2𝝅 𝒓 𝟑 V = 𝟒 𝟑 2𝝅 𝒓 𝟑 Volume of a cylinder: V = Bh V = 𝝅 𝒓 𝟐 h V = 𝝅 𝒓 𝟐 𝟐𝐫 V = 2𝝅 𝒓 𝟑 You can use the relationship between the cone and the cylinder to find the formula for volume of a sphere. How?

Volume of a sphere:

Find the volume of the sphere. Let’s practice: Find the volume of the sphere. 2 cm

Find the volume of the sphere: 8 cm

Find the radius of a sphere with volume 3052.08 cm³.

You just placed a single scoop of delicious ice cream on a sugar cone You just placed a single scoop of delicious ice cream on a sugar cone. As you are about to take the first bite, your mom asks if the ice cream can all fit inside the cone. The ice cream cone has a radius of 3 cm and a height of 10 cm. If the scoop of ice cream is a sphere with a radius of 3.5 cm, will all the ice cream fit inside the cone? If so, how much more ice cream could the cone hold? If the cone is unable to hold the ice cream, design a new ice cream cone. Be sure to include how and why you chose the new dimensions. Justify your answer with mathematics.

Classwork…. Complete the practice sheet: Volume of a Sphere. You may work with a partner, or as a group. Show ALL your work. Draw a rough sketch and then write out the formula.

Homework…. Complete the Volumes of Cones, Cylinders and Spheres problem solving worksheet. Draw a rough sketch. Write down the formula. Show all your work.