Points O and T are, respectively, the midpoints of the edges AB and CD of the rectangular

| September 30, 2021 | education

Points O and T are, respectively, the midpoints of the edges AB and CD of the rectangular parallelepiped ABCDA1B1C1D1, in which AB = 6 cm, BC = 8 cm, CC1 = 10 cm.Calculate the volume of the prism DD1C1TAA1B1O

The volume of the desired prism DD1C1TAA1O is the difference between the volume of the parallelepiped ABCD A1B1C1D1 and the prism BB1OCC1T.

V = V1 – V2.

V1 = AB * BC * CC1 = 6 * 8 * 10 = 480 cm3.

Let us determine the area of the triangle BB1O, which is the base of the triangular prism BB1OCC1T.

The triangle BB1O is rectangular, then Svv1o = OB * BB1 / 2.

BB1 = CC1 = 10 cm.

ОВ = AB / 2 = 6/2 = 3 cm, since point O is the middle of the segment AB.

Svv1o = 3 * 10/2 = 15 cm2.

Then V2 = Svv1o * BC = 15 * 8 = 120 cm3.

V = 480 – 120 = 360 cm3.

Answer: The volume of the prism is 360 cm3.



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