Question

Consider the three triangular pyramids.

Pyramid 1
Pyramid 2
Pyramid 3

Triangular pyramid 1. The base has a base of 12 meters and height of 2 meters. The height of the pyramid is 10 meters.

Triangular pyramid 2. The base has a base of 6 meters and height of 4 meters. The height of the pyramid is 10 meters.

Triangular pyramid 3. The base has a base of 12 meters and height of 4 meters. The height of the pyramid is 5 meters.

Which statement about their volumes is true? (Recall the formula V = one-third B h.)

O All three pyramids have the same volume.
O All three pyramids have different volumes.
O Only pyramids 1 and 2 have the same volume.
O Only pyramids 1 and 3 have the same volume.

Answer 1

9514 1404 393

Answer:

  (a) All three pyramids have the same volume

Step-by-step explanation:

The triangular base has an area of ...

  B = 1/2bh . . . . where b is the base of the triangle and h is its height.

The volume of the pyramid is ...

  V = 1/3BH . . . . where B is the area of the base, and H is the height of the pyramid.

Combining these equations gives ...

   V = 1/3(1/2bh)H = 1/6bhH

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Pyramid 1 volume

  V1 = 1/6(12 m)(2 m)(10 m) = 40 m³

Pyramid 2 volume

  V2 = 1/6(6 m)(4 m)(10 m) = 40 m³

Pyramid 3 volume

  V3 = 1/6(12 m)(4 m)(5 m) = 40 m³

All three pyramids have the same volume.