# Volume Of Pyramids Assignment And Quiz

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question
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?
The height of each pyramid is 1/2h units.
question
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 1/3Bh.
(b)(b) (b)(b)(b) b/2 6 (1/6)(b)(b)(2h)
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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.
52900 2645000
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If two pyramids have the same height, what must be true of the pyramids for them to also have the same volume?
The areas of the bases must be the same.
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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.
5 4 3 64
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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?
x^2(x + 2)/3 cubic inches
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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.
6 100
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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 x^2√3/4 units2. The area of the hexagon base is ______ times the area of the equilateral triangle. The volume of the pyramid is ______ x^2√33 units3.
3x area six 3/2
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What lengths would allow you to calculate the volume of the oblique pyramid with a square base? Check all that apply.
AB and EF AC, CB, and EF AD, DB, and EF
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The volume of an oblique pyramid with a square base is V units3 and the height is h units. Which expression repr
3v/h units2
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A solid oblique pyramid has a regular hexagonal base with an area of 54 cm2 and an edge length of 6 cm. Angle BAC measures 60°. What is the volume of the pyramid?
324 cm3
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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches. What is the height of the triangular base of the pyramid?
9√3 in.
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A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4√3 cm and an area of 12√3 cm2. What is the volume of the pyramid?
16√3
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The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the height of the triangular base of the pyramid?
5/2√3 units
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A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
1/3x^2y cm^3
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A right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet. The height of the pyramid is _____