This document provides calculations and explanations of various geometric concepts, including volume of pyramids, spheres, prisms, cylinders, and paving stones, as well as trigonometric calculations in right triangles.
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[...] The volume of the paving stone is 22.5 cm3. The volume of a pyramid is equal to 1/3 of the product of the area of its base multiplied by its height. The volume of the pyramid is equal to 11.25 cm3 The volume of a right prism is equal to the product of the area of its base by its height. The volume of the prism is approximately 1.13 m3. The volume of a cylinder is equal to the area of its base multiplied by its height. [...]
[...] The square of the hypotenuse is therefore equal to the sum of the squares of the two other sides, we can therefore assert that the display case is perpendicular to the wall and that consequently, the steel ball will not roll. In a right triangle, we know that the sine of an angle is equal to the adjacent side divided by the hypotenuse. The length AH is approximately 74.7 meters. We know that in a right triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse. The angle RST measures approximately 70°. The volume of a paving stone is equal to the product of its height, width, and length. [...]
