Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? V = (1/3)Bh for B

Verified step by step guidance

1. Start with the given formula: $V\; =\; (1/3)Bh$. The goal is to solve for $B$.
2. To isolate $B$, first eliminate the fraction $(1/3)$ by multiplying both sides of the equation by 3. This gives: $3V\; =\; Bh$.
3. Next, to solve for $B$, divide both sides of the equation by $h$. This results in: $B\; =\; (3V)/h$.
4. The formula $V\; =\; (1/3)Bh$ is recognized as the formula for the volume of a pyramid, where $V$ is the volume, $B$ is the area of the base, and $h$ is the height.
5. The final formula for $B$ is $B\; =\; (3V)/h$, which expresses the base area in terms of the volume and height of the pyramid.

Key Concepts

Volume of a Pyramid

The formula V = (1/3)Bh represents the volume of a pyramid, where V is the volume, B is the area of the base, and h is the height of the pyramid. This formula indicates that the volume is one-third the product of the base area and the height, reflecting how the shape of a pyramid occupies space.

Solving for a Variable

Solving for a variable involves rearranging an equation to isolate the desired variable on one side. In this case, we need to manipulate the formula V = (1/3)Bh to express B in terms of V and h, which requires understanding algebraic operations such as multiplication, division, and the properties of equality.

Area of a Base

The area of the base (B) in the context of the pyramid formula can vary depending on the shape of the base (e.g., triangular, rectangular). Understanding how to calculate the area of different geometric shapes is essential for applying the volume formula correctly and for interpreting the results in practical scenarios.