A regular triangular pyramid has a base side measuring 10 cm and the total height of the pyramid equal to 12 cm. What is the volume of this pyramid?

A colored paper sheet, in the shape of a square with sides of 20 cm, will be used to cover all faces and the base of a regular quadrangular pyramid with a height of 12 cm and a base apothem measuring 5 cm. After completing this task, and considering that there was no paper waste, the percentage fraction that will remain from this paper sheet corresponds to:

Observe, in the image, a square base pyramid sectioned by two planes parallel to the base, one containing point A and the other, point B. These planes divide each lateral edge into three equal parts. Consider the following measurements of the pyramid: • height = 9 cm; • base edge = 6 cm; • total volume = 108 cm³. The volume of the region between the parallel planes, in cm³, is:

Note that the generated frustum has a height of one third of the height of the pyramid. Its volume is given by: To calculate the areas of the bases, just apply the similarity relationship of the bases, with the larger base edge being 2/3 of the base edge of the pyramid and the upper area being 1/3 (4 and 2 centimeters). Substituting:

During a science fair, a group of 2nd-year high school students decides to build a regular square-based pyramid, where each side of the base is 10 cm and the height of the pyramid is 12 cm. The students want to fill the interior of the pyramid with sand to provide more support to the project. Calculating the necessary volume of sand in cm³ to completely fill the pyramid, we have:

During a spatial geometry class, the teacher challenged the students to calculate the volume of a square-based pyramid that was on the table. He provided the following information: the edge of the base measures 8 cm and the height of the pyramid is 12 cm. Your task is to calculate the volume of this pyramid.

Question bank: Spatial Geometry: Volume of the Pyramid

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