Volume: Cylinders, Cones, Spheres Volume is the measurement of how much 3 dimensional space is taken up by a 3 dimensional object. Area is measured in square units. Volume is measured in cubic units

A review of area of a circle Because Cylinders, Cones, and Spheres all have a circular base, and area is closely related to volume, we will need to review what we know about circles and their areas… Long ago, we discovered that whenever we took the ratio of a circle’s circumference and its diameter, we would always get the same value, no matter how large or small the circle; the value was approximately 3.14159, or 22/7 We now understand this value as the irrational number known as pi or ∏ For our purposes, when calculating values with pi, we will use either 3.14 or the ∏ button on our calculator.

Area of a Circle Although for circumference we can use the diameter, for area of a circle we will need ∏ and the radius. The radius is ½ the diameter; the diameter is 2 times the radius r = d/2 d = 2r Area is the amount of 2 dimensional space enclose within a 2 dimensional shape; measured in square units. The area of a circle = ∏r2

Model examples using area of a circle Finding area of a circle if radius is 3 units. (approx. vs in terms of pi). (turn n’ talk) Find the area of a circle with a radius of 5. (approx & in terms of pi) Finding the approximate radius if a circle’s area is approximately 100 sq. cm.

…Area of circle continued: put answers for area both as approximations to the nearest tenth place, and in terms of pi. Group A: 1.) find the area of a circle with a radius of 6 2.) find the area of a circle with a radius of 7.5 3.) find the area of a circle with a diameter of 12 Group B: 1.) find the area of a circle with a radius of 52 2.) find the area of a circle with a radius of (3/4) 3.) find the radius of a circle with an area of 80 square units Group C: 1.) find the area of a circle with a diameter of 7.4 2.) find the area of a circle with a radius of (5/3) 3.) find the area of a circle with a radius of 3x4 in terms of pi, and approximate. 4.) find the radius of a circle with an area of 29

Volume of a cylinder Like prisms, we can find the Volume of a cylinder by multiplying the area of the base, by the height of the cylinder. Volume = (Area of base)(height) V=Abh ..\..\..\Videos\Volume of Cylinder\Where Does The Volume of a Cylinder Formula Come F.mp4

Model examples: volume of a cylinder (approximate vs. in terms of pi) Finding the volume of a cylinder with a radius of 3 and height of 10 (approximate, & in terms of pi) Finding the missing height, if volume is 50, and radius is 2

…continued Finding the missing radius of a cylinder with a height of 9, and a volume of 40.

Practice with volume of a cylinder: Give volume answers as approximation to nearest tenth & in terms of ∏ Group A: 1.) Find the volume of a cylinder with a radius of 2 and a height of 7. 2.) Determine the volume of a cylinder with a radius of 2.5, and a height of 10 3.) Determine the volume of a cylinder with a diameter of 11 and a height of 15 Group B: 1.) Find the volume of a cylinder with a radius of 12 and a height of 18.5. 2.) Determine the volume of a cylinder with a radius of (5/3), and a height of 18 3.) Determine the missing height of a cylinder with a diameter of 11 and a volume of 200 Group C: 1.) Find the volume of a cylinder with a diameter of (4/3) and a height of 24. 2.) Determine the missing height of a cylinder with a diameter of 2.5, and a Volume of 19.5 3.) Determine the diameter of a cylinder with a height of 11 and a volume of 20

Volume of a Cone To understand the volume of a cone, we are first going compare a cone’s volume to, what we now know, the volume of a cylinder. Suppose we have a cone and a cylinder with the exact same radius and height. Because the cone is 1/3 the volume of the cylinder, all we have to do is multiply the volume formula for the cylinder, by 1/3.

Volume of Cone Continued Because the cone is 1/3 the volume of the cylinder, all we have to do is multiply the volume formula for the cylinder, by 1/3. But how do we know that a cone (same height & radius, is 1/3 the volume of a cylinder? ..\..\..\Videos\Volume of a Cone\Volume of a cone.mp4 ..\..\..\Videos\Volume of a Cone\Volume of Cone.mp4

Practice with volume of a cone: Give volume answers as approximation to nearest tenth & in terms of ∏ Group A: 1.) Find the volume of a cone with a radius of 2 and a height of 7. 2.) Determine the volume of a cone with a radius of 8.5, and a height of 11 3.) Determine the volume of a cone with a diameter of 14 and a height of 8 Group B: 1.) Find the volume of a cone with a radius of 9 and a height of 6.3. 2.) Determine the volume of a cone with a radius of (2/3), and a height of 6 3.) Determine the missing height of a cone with a diameter of 8 and a volume of 200 Group C: 1.) Find the volume of a cone with a diameter of (4/5) and a height of 24. 2.) Determine the missing height of a cone with a diameter of 18.7, and a Volume of 23.3 3.) Determine the diameter of a cone with a height of 11 and a volume of 22

Volume of a Sphere (from cone/cylinder) Show videos first (video folder)

Volume of a Sphere

Practice with volume of a sphere: Give volume answers as approximation to nearest tenth & in terms of ∏ Group A: 1.) Find the volume of a sphere with a radius of 4. 2.) Determine the volume of a sphere with a radius of 2.5. 3.) Determine the volume of a sphere with a diameter of 13. Group B: 1.) Find the volume of a sphere with a radius of 12. 2.) Determine the volume of a sphere with a radius of (2/3). 3.) Determine the combined volume of 3 spheres of the same size, having a diameter of 7. Group C: 1.) Find the volume of a sphere with a diameter of (8/3). 2.) Find the volume of a ½ sphere with a diameter of 9. 2.) Determine the missing diameter of a sphere with a volume of 27

Homework: #10: read p302, do quickcheck #2a, 2b. #11:

Spring Break Homework 2017 All to be done in our workbook Course 3 Mathematics Common Core (looks just like text book, but soft cover) Work must be shown for relevant problems. p107 all p127 odds P131 odds P133 odds P135 odds P179 odds P181 odds P183 odds