From a triangular prism, the volume of which is 15, a triangular pyramid is cut

| May 3, 2021 | education

From a triangular prism, the volume of which is 15, a triangular pyramid is cut off by a plane passing through the side of one base and the opposite vertex of the other base. Find the volume of the remainder.

Let’s use the picture to solve the problem.

The base area ABC of the pyramid and the prism are equal to each other and lie in the same plane. The pyramid and the prism have a common vertex at point A1, therefore the height AA1 of the pyramid and the prism is also common.

Let’s use the formulas for the volume of a prism and a pyramid.

Vpr = Sadc * AA1.

Vpyr = Sadc * AA1 / 3.

Let’s find the ratio of the volume of the prism to the volume of the pyramid.

Vpr / Vpyr = Sadc * AA1 / = Sadc * AA1 / 3 = 3.

Then Vpir = 15/3 = 5 cm3.

The volume of the remaining part is equal to:

V = Vpr – Vpir = 15 – 5 = 10 cm3.

Answer: The volume of the remaining part is 10 cm3.



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