Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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1:24 minutes

Problem 38

Textbook Question

In Exercises 35–54, 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

Start with the given formula:

V = (1/3)Bh

. The goal is to solve for

B

To isolate

B

, first eliminate the fraction

(1/3)

by multiplying both sides of the equation by 3. This gives:

3V = Bh

Next, to solve for

B

, divide both sides of the equation by

h

. This results in:

B = (3V)/h

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.

The final formula for

B

B = (3V)/h

, which expresses the base area in terms of the volume and height of the pyramid.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.