COMO HALLAR O CALCULAR LA GENERATRIZ DE UN CONO TRUNCADO

Summary

In this tutorial, Professor Edinson.net explains how to calculate the generatrix length of a truncated cone using the Pythagorean theorem. The example provided involves a truncated cone with a larger radius of 10 cm, a smaller radius of 6 cm, and a height of 18 cm. By drawing a right triangle and applying the Pythagorean theorem, the length of the generatrix is calculated to be approximately 18.44 cm. This step-by-step guide helps students understand the process clearly, and the video encourages viewers to share and subscribe for more educational content.

Takeaways

• 😀 The tutorial explains how to calculate the length of the generatrix of a truncated cone.
• 😀 The required known values to calculate the generatrix are the larger radius, smaller radius, and the height of the cone.
• 😀 The larger radius (R) of the truncated cone is 10 cm, the smaller radius (r) is 6 cm, and the height (h) is 18 cm.
• 😀 To find the generatrix, a right triangle is formed where the height of the cone acts as one side, and the difference between the radii as the other side.
• 😀 The length of the difference between the radii (R - r) is calculated as 4 cm (10 cm - 6 cm).
• 😀 The Pythagorean theorem is used to calculate the hypotenuse (the generatrix) of the right triangle.
• 😀 The Pythagorean theorem formula is: G² = 18² + 4².
• 😀 After calculating the squares, the sum is 340 cm², which leads to the equation: G² = 340 cm².
• 😀 Taking the square root of both sides, the length of the generatrix (G) is approximately 18.44 cm.
• 😀 The tutorial emphasizes the simplicity of using the Pythagorean theorem to solve for the generatrix of a truncated cone.

Q & A

What is the main topic of the video tutorial?

The video tutorial explains how to calculate the length of the generatrix of a truncated cone, given the lengths of the major and minor radii, as well as the height of the cone.

What is the formula used to calculate the length of the generatrix?

The formula used is based on the Pythagorean theorem. The length of the generatrix (G) is calculated by taking the square root of the sum of the squares of the height and the difference between the major and minor radii.

What information is required to calculate the length of the generatrix?

You need the lengths of the major radius, the minor radius, and the height of the truncated cone.

How do you find the horizontal distance (cathetus) used in the Pythagorean theorem?

The horizontal distance is the difference between the major and minor radii. For example, if the major radius is 10 cm and the minor radius is 6 cm, the horizontal distance is 10 cm - 6 cm = 4 cm.

What is the significance of the Pythagorean theorem in this calculation?

The Pythagorean theorem helps to find the length of the generatrix by relating the height (one cathetus) and the horizontal distance (the other cathetus) to the generatrix, which is the hypotenuse of a right triangle.

What is the value of the generatrix after applying the Pythagorean theorem in this example?

After applying the Pythagorean theorem, the length of the generatrix is approximately 18.44 cm.

How do you calculate the square of a number in the context of this tutorial?

To calculate the square of a number, you multiply the number by itself. For example, 18 cm squared is 18 cm × 18 cm = 324 cm².

What is the importance of the square root in this process?

The square root is used to find the length of the generatrix after summing the squares of the height and the horizontal distance. Taking the square root of the sum gives the exact length of the generatrix.

Why is the minor radius subtracted from the major radius?

The minor radius is subtracted from the major radius to calculate the horizontal distance between the two radii, which is one of the catheti in the right triangle used in the Pythagorean theorem.

What is the final step after calculating the sum of the squares?

The final step is to take the square root of the sum of the squares to determine the length of the generatrix. In this case, the square root of 340 cm² is approximately 18.44 cm.