Math Problem Statement
Solve the equation V = 1/3 π r^2 (h - l) for h.
Solution
The equation provided in the image is:
You are asked to "get h alone", meaning we need to solve the equation for h. Let's work through it step by step.
Step 1: Start with the given equation
Step 2: Eliminate the fraction
Multiply both sides of the equation by 3 to remove the fraction:
Step 3: Isolate the term involving h
Divide both sides by :
Step 4: Solve for h
Add l to both sides to isolate h:
Thus, the equation solved for h is:
Would you like more details, or do you have any questions?
Here are five related questions:
- What does the variable V represent in this context?
- How does the radius r affect the height h in this formula?
- Can this formula be applied to calculate the height of a cone given its volume?
- What units would typically be used for each variable in this formula?
- How would the equation change if the cone had a slant height instead of a vertical height?
Tip: Always check the dimensions or units of each variable to ensure consistency when solving physics or geometry problems.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Formulas
V = 1/3 π r^2 (h - l)
h = (3V / πr^2) + l
Theorems
Volume of a Cone
Algebraic Rearrangement
Suitable Grade Level
Grades 9-11