Question bank: Spatial Geometry: Volume of the Pyramid

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Question 1:

Medium

A toy company decided to create plastic pyramids for a new educational kit. The mold for making this pyramid is a solid with a square base measuring 8 cm on each side and a height of 15 cm. The manufacturing process of the pyramid involves completely filling the mold with liquid plastic, which is then cooled to acquire the solid form. As the head of the production department, you need to calculate the amount of plastic needed to produce each pyramid. What is the volume of plastic needed, in cubic centimeters, to produce a single pyramid?

Spatial Geometry: Volume of the Pyramid

Question 2:

Very Easy

A regular square pyramid has a base that is a square with a side length of 6 cm and a height of 8 cm. Calculate the volume of this pyramid using the formula V = (A * h) / 3, where V is the volume, A is the base area, and h is the pyramid's height. Use the formula for the area of a square A = L^2, where L is the side length of the square.

Spatial Geometry: Volume of the Pyramid

Contextualized Question

Calculus Question

Question 3:

Hard

Spatial Geometry: Volume of the Pyramid

Basic Calculus

Question 4:

Medium

A regular pyramid with a square base has all edges of its base measuring 'a' and its height 'h'. The pyramid is made of glass and will be used as a model in an Arts class to study the propagation of light through different materials. To calculate the amount of light that will pass through the pyramid, it is necessary to know its volume. Considering the interdisciplinary application of Spatial Geometry with Optical Physics, determine the volume of the pyramid and explain how the solid's geometry influences the propagation of light inside it, mentioning at least one concept of Optical Physics that can be related to the geometric characteristics of the pyramid.

Spatial Geometry: Volume of the Pyramid

Multidisciplinary Question

Question 5:

Medium

In an international architecture competition, a group of students designed a pyramidal structure for a new museum. The pyramid has a quadrangular prism as its base, with sides measuring 40 meters, and its height is 45 meters. What is the volume of this pyramid designed by the students?

Spatial Geometry: Volume of the Pyramid

IARA TIP

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