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?

answer

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.

answer

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

question

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.

answer

52900
2645000

question

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

answer

The areas of the bases must be the same.

question

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.

answer

5
4
3
64

question

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?

answer

x^2(x + 2)/3 cubic inches

question

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 β ACB is 45Β°.
The height, AB, is __ cm.
The volume of the pyramid is ___ cm3.

answer

6
100

question

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^2β3/4 units2.
The area of the hexagon base is ______ times the area of the equilateral triangle.
The volume of the pyramid is ______ x^2β33 units3.

answer

3x
area
six
3/2

question

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

answer

AB and EF
AC, CB, and EF
AD, DB, and EF

question

The volume of an oblique pyramid with a square base is V units3 and the height is h units.
Which expression repr

answer

3v/h units2

question

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 60Β°.
What is the volume of the pyramid?

answer

324 cm3

question

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?

answer

9β3 in.

question

A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4β3 cm and an area of 12β3 cm2.
What is the volume of the pyramid?

answer

16β3

question

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?

answer

5/2β3 units

question

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?

answer

1/3x^2y cm^3

question

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 _____

answer

16 ft

question

The oblique pyramid has a square base.
The volume of the pyramid is ____ cm3.

answer

5

question

The volume of a solid right pyramid with a square base is V units3 and the length of the base edge is y units.
Which expression represents the height of the pyramid?

answer

3V/y^2 units

question

A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches.
Which expression shows the area of the base of each pyramid?

answer

(1/4x)^2 in2