Volume de pirâmide - Brasil Escola

Brasil Escola Oficial
24 Feb 202107:22

Summary

TLDRIn this math lesson, the teacher explains how to calculate the volume of a pyramid. By comparing a pyramid with a rectangular base to a rectangular prism, the teacher demonstrates that the volume of the pyramid is one-third of the volume of the prism. Using a clear example with a regular square-based pyramid, the teacher walks through the steps: calculating the area of the base, multiplying by the height, and dividing by three to get the volume. The video also suggests reviewing previous lessons on pyramid areas for a better understanding.

Takeaways

  • 😀 The volume of a pyramid is calculated using the formula: Volume = (Area of base * Height) / 3.
  • 😀 To understand the volume relationship between a pyramid and a prism, the volume of a prism is three times that of a pyramid with the same base area and height.
  • 😀 The formula for the volume of a pyramid is derived from the fact that three pyramids with the same base area and height can fit into a prism.
  • 😀 The volume of a pyramid is always one-third of the volume of a corresponding prism, where the prism has the same base and height as the pyramid.
  • 😀 The area of the base of a pyramid can be calculated first, then multiplied by the pyramid's height to find the volume before dividing by 3.
  • 😀 The script uses a practical example of a pyramid with a square base to explain the volume calculation.
  • 😀 In the example, the diagonal of the square base is given as 24√2 cm, and from this, the side of the square can be determined.
  • 😀 To calculate the area of the base for a square pyramid, the side length is squared, and then the result is used in the volume formula.
  • 😀 In the example, after calculating the area of the square base and multiplying it by the height of the pyramid, the final volume is obtained by dividing by 3.
  • 😀 The final volume of the pyramid in the example is found to be 3,072 cubic centimeters, demonstrating the application of the formula.

Q & A

  • What is the main topic of this lesson?

    -The main topic of the lesson is how to calculate the volume of a pyramid.

  • How do we calculate the volume of a pyramid in this video?

    -The volume of a pyramid is calculated as one-third of the base area times the height, which is expressed as: Volume = (Base Area * Height) / 3.

  • What visual aid does the teacher use to explain the concept?

    -The teacher uses a visual comparison between a rectangular prism and a pyramid, showing how three pyramids can fit inside the prism, illustrating the relationship between their volumes.

  • What formula is derived to calculate the volume of a pyramid?

    -The formula derived for the volume of a pyramid is: Volume = (Base Area * Height) / 3.

  • What is the significance of the number three in the volume calculation?

    -The number three signifies that the volume of the pyramid is one-third of the volume of a prism with the same base area and height. This is why the pyramid's volume is calculated by dividing the prism's volume by three.

  • How does the teacher suggest remembering the formula for the volume of a pyramid?

    -The teacher suggests remembering that the volume of a pyramid is one-third of the volume of a prism, and that the formula is: Volume = (Base Area * Height) / 3.

  • What exercise does the teacher work through in the video?

    -The teacher works through an exercise where the base of a pyramid is a square, and the diagonals of the base are 24√2 cm. The height of the pyramid is 16 cm, and the goal is to calculate the volume of the pyramid.

  • How does the teacher calculate the side length of the square base?

    -The teacher uses the fact that the diagonal of a square is equal to the side length times the square root of 2. Given the diagonal is 24√2 cm, the teacher simplifies it to find that the side length of the square is 24 cm.

  • What steps are involved in calculating the volume of the pyramid in the exercise?

    -First, the side length of the square base is found (24 cm). Then, the area of the base is calculated by squaring the side length (24 * 24). Finally, the area is multiplied by the height of the pyramid (16 cm) and divided by three to find the volume.

  • What is the final volume of the pyramid in the exercise?

    -The final volume of the pyramid is 3,072 cubic centimeters.

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Math TutorialVolume CalculationPyramid FormulaGeometryMathematicsMath EducationVolume of PyramidMath ExampleStep-by-StepGeometry LessonMathematics Teaching
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