Volume of Pyramids

Question 1

Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid?

Revolt · Accepted Answer

The height of each pyramid is h units.

Question 2

The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge.

Revolt · Accepted Answer

The height of the pyramid can be represented as .: 3x; The of an equilateral triangle with length x is units2.: area; The area of the hexagon base is times the area of the equilateral triangle.: six; The volume of the pyramid is x3 units3.: 3/2

Question 3

(b)(b/2)✔ (b)(b)(b)(b)(b)

Revolt · Accepted Answer

✔ (b)(b); The area of the base of the cube, B, is square units.: (b)(b); The volume of the cube is cubic units.: (b)(b)(b); The height of each pyramid, h, is . Therefore,: b/2; There are square pyramids with the same base and height that exactly fill the given cube.: 6; Therefore, the volume of one pyramid is or Bh.: (1/6)(b)(b)(2h)

Question 4

✔ (b)(b)(b)(b)(b)(b/2)(b)(b)(b/6)

Revolt · Accepted Answer

✔ (b)(b)(b)

Question 5

✔ b/2b2b

Revolt · Accepted Answer

✔ b/2

Question 6

24✔ 6

Revolt · Accepted Answer

✔ 6

Question 7

(1/6)(b)(b)(h)✔ (1/6)(b)(b)(2h)(1/6)(2b)(h)

Revolt · Accepted Answer

✔ (1/6)(b)(b)(2h)

Question 8

The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.

Revolt · Accepted Answer

✔ 52,900; The area of the base is m2.: 52,900; The volume is m3.: 2,645,000

Question 9

7,93552,900✔ 2,645,0007,935,000

Revolt · Accepted Answer

✔ 2,645,000

Question 10

If two pyramids have the same height, what must be true of the pyramids for them to also have the same volume?

Revolt · Accepted Answer

The areas of the bases must be the same.

Volume of Pyramids Answers

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