The height of the pyramid is 16 cm, and the base area is 512 cm. At what distance from the base is the section

| March 8, 2021 | education

The height of the pyramid is 16 cm, and the base area is 512 cm. At what distance from the base is the section parallel to the base if the section area is 50 cm.

Section A1B1C1 is parallel to the base of the ABC pyramid, then it cuts off the pyramid A1B1C1D similar to the original pyramid from the ABCD pyramid.

Since the pyramids are similar, their bases ABC and A1B1C1 are similar triangles, the areas of which are related as the square of the coefficient of similarity.

Then Savs / Sa1v1s1 = K2 = 512/50 = 256/25.

K = 16/5.

The ratio of the heights of the pyramids is equal to the coefficient of similarity.

DO / DO1 = 16/5.

DO1 = DO / (16/5) = 16 / (16/5) = 5 cm.

Then OO1 = DO – DO1 = 16 – 5 = 11 cm.

Answer: From the base of the pyramid to a section of 11 cm.



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