Area of a Circle and a Sector Answers

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?

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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.

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.

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

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.

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?

The area of the base of the oblique pentagonal pyramid is 50 cm2 and the distance from the apex to the center of the pentagon is 6 cm. The measure of ∠ACB is 45°. The height, AB, is cm. The volume of the pyramid is cm3.

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

What lengths would allow you to calculate the volume of the oblique pyramid with a square base? Check all that apply.

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