Solve Volume Formulas for Specific Variables
Solving volume formulas for specific variables is a Grade 7 algebra and geometry skill in Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume. Isolating a specific variable in a volume formula requires the same inverse operations used in equation solving. For the pyramid volume formula V equals one-third B h, solving for h gives h equals 3V divided by B by multiplying both sides by 3 and dividing by B.
Key Concepts
To solve a formula for a specific variable means to isolate that variable on one side of the equals sign with a coefficient of one. All other variables and constants are moved to the other side of the equal sign. For example, to solve the pyramid volume formula $V = \frac{1}{3}Bh$ for $h$, you would perform the following steps: 1. Write the formula: $V = \frac{1}{3}Bh$ 2. Remove the fraction by multiplying both sides by 3: $3V = Bh$ 3. Isolate $h$ by dividing both sides by $B$: $\frac{3V}{B} = h$.
Common Questions
How do you solve a volume formula for a specific variable?
Use inverse operations to isolate the target variable. Multiply, divide, add, or subtract to move all other terms to the other side, keeping the equation balanced throughout.
How do you solve V equals one-third B h for h?
Multiply both sides by 3 to get 3V equals B h, then divide both sides by B to get h equals 3V divided by B.
Why is it useful to rearrange volume formulas?
Rearranging a formula for a specific variable creates a direct tool for finding that measurement. Instead of solving step-by-step each time, you can substitute known values directly into the rearranged formula.
What textbook covers solving volume formulas for variables in Grade 7?
Big Ideas Math Advanced 2, Chapter 14: Surface Area and Volume covers rearranging volume formulas to solve for dimensions like height and base area.