Algebraic Manipulation Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Rearrange V=13ฯ€r2hV = \frac{1}{3}\pi r^2 h to solve for hh.

Solution

  1. 1
    Multiply both sides by 3: 3V=ฯ€r2h3V = \pi r^2 h.
  2. 2
    Divide by ฯ€r2\pi r^2: h=3Vฯ€r2h = \frac{3V}{\pi r^2}.

Answer

h=3Vฯ€r2h = \frac{3V}{\pi r^2}
Isolating a variable in a formula requires reversing operations. Multiply to clear fractions, then divide to isolate the target variable. This skill is essential in science and engineering.

About Algebraic Manipulation

Algebraic manipulation is the process of rewriting expressions or equations into equivalent forms to reveal structure or solve for unknowns.

Learn more about Algebraic Manipulation โ†’

More Algebraic Manipulation Examples

Example 1 easy

Simplify [formula].

Example 2 medium

Solve for [formula]: [formula].

Example 3 easy

Simplify [formula].

โ† All Algebraic Manipulation Examples Algebraic Manipulation Concept