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

✔ b/2b2b

Revolt · Accepted Answer

b/2

Question 3

24✔ 6

Revolt · Accepted Answer

6

Question 4

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

Revolt · Accepted Answer

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

Question 5

The area of the base of the cube, B, is square units. The volume of the cube is cubic units. The height of each pyramid, h, is . Therefore, b = 2h. There are square pyramids with the same base and height that exactly fill the given cube. Therefore, the volume of one pyramid is or Bh.

Revolt · Accepted Answer

(b)(b); Selection 1: (b)(b); Selection 2: (b)(b)(b); Selection 3: b/2; Selection 4: 6; Selection 5: (1/6)(b)(b)(2h)

Question 6

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 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 7

✔ (b)(b)(b)(b)(b)(b/2)(b)(b)(b/6)

Revolt · Accepted Answer

✔ (b)(b)(b)

Question 8

The height of each pyramid, h, is [___]. Therefore,

Revolt · Accepted Answer

b/2

Question 9

24✔ 6

Revolt · Accepted Answer

✔ 6

Question 10

Therefore, the volume of one pyramid is [___] or Bh.

Revolt · Accepted Answer

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

Volume of Pyramids Answers

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