A triangular prism has a height of 10 cm and a base area of 12 cm2. A rectangular prism has a height of 10 cm and base dimensions of 3 cm and 4 cm. Do the solids have the same volume?. A ... Yes, because they have the same height and the same cross sectional area at every level parallel to the bases ... B ... Yes, because they are congruent solids ... C ... No, because Cavalieri's principle only applies to solids with congruent cross sections ... D ... No, because they have different dimensions ...

Question

Mathematics

Madeline

11 December, 21:41

A triangular prism has a height of 10 cm and a base area of 12 cm2. A rectangular prism has a height of 10 cm and base dimensions of 3 cm and 4 cm. Do the solids have the same volume?. A ... Yes, because they have the same height and the same cross sectional area at every level parallel to the bases ... B ... Yes, because they are congruent solids ... C ... No, because Cavalieri's principle only applies to solids with congruent cross sections ... D ... No, because they have different dimensions ...

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Answers (1)

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Kaleb Adams · Answer 1

V triangular prism = (10 x12) / 3 = 120 / 3 = 40 cm^3;

The base area of rectangle is 3 x 4 = 12 cm^2;

V rectangular prism = (10x12) / 3 = 40 cm^3;

The solids have the same volume!

Two solids are congruent if all their angles, edges, and faces are congruent.

Finally, the right answer is A.