What does the variable 'B' represent in the formula for the volume of a pyramid?

What does the variable 'B' represent in the formula for the volume of a pyramid?

• A. The base area of the pyramid
• B. The height of the pyramid
• C. The lateral surface area
• D. The diameter of the base

Answer: (A)

In the formula for the volume of a pyramid, the variable 'B' specifically denotes the area of the base of the pyramid. The volume calculation of a pyramid is given by the formula: \[ V = \frac{1}{3} \times B \times h \] where \( V \) represents the volume, \( B \) is the area of the base, and \( h \) is the height of the pyramid. This relationship indicates that the volume is directly proportional to the size of the base area and the height. Understanding the significance of the base area is crucial because the volume is dependent on how much space is enclosed by the pyramid, which ties directly to the shape and size of its base. If the area of the base changes, it directly affects the total volume regardless of the height. Hence, recognizing 'B' as the base area is key to grasping how the volume of a pyramid is derived and calculated.

In the formula for the volume of a pyramid, the variable 'B' specifically denotes the area of the base of the pyramid. The volume calculation of a pyramid is given by the formula:

[

V = \frac{1}{3} \times B \times h

]

where ( V ) represents the volume, ( B ) is the area of the base, and ( h ) is the height of the pyramid. This relationship indicates that the volume is directly proportional to the size of the base area and the height.

Understanding the significance of the base area is crucial because the volume is dependent on how much space is enclosed by the pyramid, which ties directly to the shape and size of its base. If the area of the base changes, it directly affects the total volume regardless of the height. Hence, recognizing 'B' as the base area is key to grasping how the volume of a pyramid is derived and calculated.