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

Question 2

Revolt · Accepted Answer

(b)(b)(b)

Question 3

Question 3

Revolt · Accepted Answer

b/2

Question 4

Question 4

Revolt · Accepted Answer

6

Question 5

Question 5

Revolt · Accepted Answer

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

Question 6

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 7

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. The area of the base is m2. The volume is m3.

Revolt · Accepted Answer

52,900; Selection 1: 52,900; Selection 2: 2,645,000

Question 8

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.

Question 9

Kabir wants to know the volume of a solid right pyramid with a square base. He uses a ruler to measure the length of the base as 8 inches. He then measures the slant height to be 5 inches. The hypotenuse of the right triangle used to determine the height is inches. The leg of the right triangle that lies on the same plane as the base is inches. The height of the pyramid is inches. The volume of the solid pyramid is cubic inches.

Revolt · Accepted Answer

5; The hypotenuse of the right triangle used to determine the height is inches.: 5; The leg of the right triangle that lies on the same plane as the base is inches.: 4; The height of the pyramid is inches.: 3; The volume of the solid pyramid is cubic inches.: 64

Question 10

A right pyramid with a square base has a base length of x inches, and the height is two inches longer than the length of the base. Which expression represents the volume in terms of x?

Revolt · Accepted Answer

cubic inches

Volume of Pyramids Answers

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