VOLUMEN DEL CONO Super Facil - Para principiantes

Daniel Carreón

29 Jan 201905:19

Summary

TLDRIn this video, Daniel Carrión explains how to calculate the volume of a cone, comparing it to a cylinder for clarity. He begins with a basic overview of volume and introduces the formula for calculating the volume of a cone, emphasizing the role of the base area and height. Through practical examples, he demonstrates how to compute the volume of cones with different dimensions, using step-by-step calculations. The video aims to make the concept of calculating cone volume easy to understand and encourages viewers to practice with additional exercises.

Takeaways

😀 The volume of a cone is calculated using the formula: Volume = (Area of the base × Height) / 3.
😀 The volume of a cylinder is calculated with the formula: Volume = Area of the base × Height.
😀 A cone's volume is always one-third of the volume of a cylinder with the same base and height.
😀 The area of the base of a cone is calculated using the formula: Area = π × radius².
😀 In the first example, a cone with a radius of 10 cm and a height of 20 cm has a volume of 2,094.4 cubic centimeters.
😀 In the second example, a cone with a diameter of 14 cm and a height of 11 cm has a volume of 564.41 cubic centimeters.
😀 The radius of a cone is half of its diameter, so a diameter of 14 cm gives a radius of 7 cm.
😀 To find the volume of a cone, first calculate the area of its base and then multiply by the height before dividing by 3.
😀 The script encourages viewers to solve practice exercises and share their answers in the comments.
😀 The video includes clear examples to help viewers understand how to apply the volume formula for a cone.

Q & A

What is the definition of volume as explained in the video?
-Volume is the space occupied by an object, or how many cubes of a certain size fit inside that object.
What is the formula for calculating the volume of a cylinder?
-The volume of a cylinder is calculated by multiplying the area of the base by the height of the cylinder.
How is the volume of a cone different from that of a cylinder?
-The volume of a cone is calculated using the same formula as a cylinder, but it is divided by 3 to account for the cone's shape.
What was demonstrated using the three cones and one cylinder?
-The demonstration showed that when cones with the same base and height as a cylinder are filled with liquid, the volume of the cone is one-third of the cylinder's volume.
What parts of a cone must be known to calculate its volume?
-To calculate the volume of a cone, you need to know the radius of the base and the height of the cone.
How do you calculate the area of the base of a cone?
-The area of the base of a cone is calculated by multiplying pi by the square of the radius of the base.
What is the result of the volume calculation for the first cone example with a radius of 10 cm and a height of 20 cm?
-The volume of the first cone is 2,094.4 cubic centimeters.
How is the area of the base calculated when the diameter is given, as in the second cone example?
-The radius is half the diameter, so the radius is 7 cm. The area of the base is then calculated by multiplying pi by 7 squared (49).
What is the volume of the second cone with a diameter of 14 cm and a height of 11 cm?
-The volume of the second cone is 564.41 cubic centimeters.
What does the presenter encourage viewers to do at the end of the video?
-The presenter encourages viewers to like, comment, share, and subscribe to the channel to continue watching future videos.