Math Problem Statement

V = πr²h is an equation to calculate the volume of a cylinder, V, where r represents the radius of the cylinder and h represents its height. Write an equation that would allow us to easily find the height of the cylinder because it is solved for h?

Solution

The problem asks to write an equation that would allow us to easily find the height hh of a cylinder, given the volume equation for a cylinder:

V=πr2hV = \pi r^2 h

where:

  • VV is the volume of the cylinder,
  • rr is the radius of the cylinder,
  • hh is the height of the cylinder.

To solve for the height hh, we can rearrange the equation by isolating hh on one side:

h=Vπr2h = \frac{V}{\pi r^2}

This equation allows us to calculate the height of the cylinder if we know the volume VV and the radius rr.

Would you like further details or have any questions about this process?

Here are 5 related questions:

  1. How do you calculate the volume of a cylinder if both height and radius are given?
  2. What happens to the height if the volume increases but the radius stays the same?
  3. Can the formula for the volume of a cylinder be applied to a cone? Why or why not?
  4. How would you calculate the radius of a cylinder if you only know the volume and height?
  5. What is the physical interpretation of πr2\pi r^2 in the volume formula?

Tip: Always double-check your units when solving for volume, height, or radius to ensure they are consistent.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Volume of Cylinder

Formulas

V = πr²h
h = V / (πr²)

Theorems

Cylindrical Volume Formula

Suitable Grade Level

Grades 8-10