Here are two formulas for the volume of a cylinder:

Question

"V" equals pi "r" squared times "h"
V=πr2·h
"V" equals "B" times "h"
V=B·h

Describe how the formulas are related simply

Answer 1

The two formulas for the volume of a cylinder are related through the concept of the base area of the cylinder.

1. First Formula: \( V = \pi r^2 \cdot h \)

   • Here, \( \pi r^2 \) represents the area of the circular base of the cylinder (where \( r \) is the radius of the base). The volume is obtained by multiplying the base area by the height \( h \).

2. Second Formula: \( V = B \cdot h \)

   • In this formula, \( B \) stands for the area of the base. For a cylinder with a circular base, \( B = \pi r^2 \).

In essence, both formulas describe how to calculate the volume of a cylinder by multiplying the area of its base by its height. The first formula explicitly represents the base area using the formula for the area of a circle, while the second formula uses the more general notation \( B \) for the base area.