Question

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A rectangular prism with a square base is cut from the center of a triangular prism. Each side of the square base measures 1.7 units.



What is the volume of the shaded solid? Round to the nearest tenth of a cubic unit.

Answer 1

First we want to calculate the volume of the rectangular prism and subtract it from the triangular prism.

Volume of Rectangular Prism:

Let V1 be the volume of the rectangular prism.

V1 = base * height * length.

The base and the height are both 1.7, but the length is the same length of the triangular prism, which is 4. Thus:

V1 = 1.7 X 1.7 X 4

V1 = 11.56 cubic units

Volume of Triangular Prism:

Let V2 be the volume of the triangular prism:

V2 = (base X height X length) / 2

V2 = (5 X 5.7 X 4)/2

V2 = 57 cubic units.

Now we find the total volume. Let Vt be the total volume. The total volume is the shaded minus the unshaded. Thus:

Vt = V2 - V1

Vt = 57 cubic units - 11.56 cubic units

Vt = 45. 44 cubic units

Therefore the volume of the shaded region is 45.44 cubic units.

Answer 2

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