Math Problem Statement

Solve the equation V = 1/3 π r^2 (h - l) for h.

Solution

The equation provided in the image is:

V=13πr2(hl)V = \frac{1}{3} \pi r^2 (h - l)

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

V=13πr2(hl)V = \frac{1}{3} \pi r^2 (h - l)

Step 2: Eliminate the fraction

Multiply both sides of the equation by 3 to remove the fraction: 3V=πr2(hl)3V = \pi r^2 (h - l)

Step 3: Isolate the term involving h

Divide both sides by πr2\pi r^2: 3Vπr2=hl\frac{3V}{\pi r^2} = h - l

Step 4: Solve for h

Add l to both sides to isolate h: h=3Vπr2+lh = \frac{3V}{\pi r^2} + l

Thus, the equation solved for h is: h=3Vπr2+lh = \frac{3V}{\pi r^2} + l

Would you like more details, or do you have any questions?

Here are five related questions:

  1. What does the variable V represent in this context?
  2. How does the radius r affect the height h in this formula?
  3. Can this formula be applied to calculate the height of a cone given its volume?
  4. What units would typically be used for each variable in this formula?
  5. 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