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Volume of Cylinders, Cones & Spheres
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What you will learn from this videoWhat you will learn
- How to find the volume of cones, cylinders, and spheres.
- How their volumes are related to one another.
- How this knowledge can help us bake a cake, take care of pets, and go for a run!
- Discussion Questions
Before Video
What is volume? What units do you use for volume?
ANSWERVolume measures the amount of space inside a 3D object. It is measured in cubic units.
42 cm^{3}. I used the formula volume equals length times width times height.
ANSWERPi is an irrational number. It is approximately 3.14. It is the ratio between the circumference and the diameter of a circle. It is represented by the symbol π.
A radius is a line from the center of a circle to its edge. A diameter is a line across a circle that passes through the center of the circle.
25π cm^{2} or about 78.5 cm^{2}
After Video
What is the formula for the volume of a cylinder? What does each part of the formula mean?ANSWERV = πr^{2}h. r is the radius of the circular base of the cylinder and h is the height of the cylinder (the distance between the two circular ends).
V = [ggfrac]1/3[/ggfrac]πr^{2}h. r is the radius of the circle at the base and h is the distance between the center point of the circular base and the point at the top of the cone.
V = [ggfrac]4/3[/ggfrac]πr^{3}. If I cut the sphere exactly in half I could see a circle on the face. r is the radius of the circle at the very center of the sphere.
360π cm^{3} or about 1,130.4 cm^{3}.
The cylinder.
- Vocabulary
- Volume DEFINE
The amount of space inside a 3D object.
- Cone DEFINE
A 3D shape with one circular base.
- Cylinder DEFINE
A 3D shape with two circular bases.
- Sphere DEFINE
A 3D shape in the shape of a ball.
- Pi (π) DEFINE
The ratio of the circumference of a circle to its diameter. This is always the same number: approximately 3.14. The actual number is an irrational number (a decimal that never ends or repeats).
- Radius DEFINE
The measurement from the center of a circle or sphere to its edge. The radius is half the diameter.
- Diameter DEFINE
The distance straight across a circle or sphere. The diameter always passes through the center point of the circle.
- Volume DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide