Question

Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b.The area of the base of the cube, B, is square units.The volume of the cube is blank cubic units.The height of each pyramid, h, is blank . 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 blank or One-third.

Answer 1

The question addresses calculating the volume of pyramids inside a cube. The cube's volume is V = b³ and since there are six pyramids in the cube, the volume of one pyramid is ⅓ × B × h.

Step-by-step explanation:

Understanding the Volume of Pyramids within a Cube

The question focuses on the mathematical concept related to geometric solids, specifically on how to calculate the volume of pyramids contained within a cube. The cube's volume is given by the formula V = b³, where b is the length of a side. When it is mentioned that b = 2h, this implies that the base b of the cube is twice the height h of the pyramids inside. Since the cube's volume is also equal to B × h (where B is the base area), and there are six pyramids within the cube, the volume of one pyramid is one-sixth of the cube's volume. This can also be expressed as Volume of one pyramid = ⅓ × B × h, which stems from the general formula for the volume of a pyramid V = ⅓Bh. Therefore, the volume of one pyramid is one-third of the volume of a prism (or cube) with the same base and height.

Answer 2

Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b. The area of the base of the cube,

B, is (b)(b) square units.

The volume of the cube is (b)(b)(b) cubic units.

The height of each pyramid, h, is b/2

b = 2h.

There are 6 square pyramids with the same base and height that exactly fill the given cube.

Therefore, the volume of one pyramid is (1/6)(b)(b)(2h)

or One-thirdBh.

Step-by-step explanation: