Calculating the Height of a Cylinder

Oct 13, 2025 by miodeya.com 94 views

**Understanding the Volume of a Cylinder: A Step-by-Step Guide** ===========================================================

What is the Volume of a Cylinder?

The volume of a cylinder is a fundamental concept in mathematics, particularly in geometry. It is defined as the amount of space inside the cylinder. The formula for the volume of a cylinder is given by:

V = πr^2h

where V is the volume, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the base of the cylinder, and h is the height of the cylinder.

Calculating the Height of a Cylinder

In the given problem, James is asked to calculate the height of a cylinder with a volume of 324π cubic inches and a radius of 12 inches. Let's break down the steps involved in solving this problem.

Step 1: Write Down the Formula for the Volume of a Cylinder

The formula for the volume of a cylinder is given by:

V = πr^2h

In this case, the volume (V) is 324π cubic inches, the radius (r) is 12 inches, and we need to find the height (h).

Step 2: Plug in the Values into the Formula

Substitute the given values into the formula:

324π = π(12)^2h

Step 3: Simplify the Equation

Simplify the equation by evaluating the expression inside the parentheses:

324π = π(144)h

Step 4: Divide Both Sides by π

Divide both sides of the equation by π to get rid of the π term:

324 = 144h

Step 5: Divide Both Sides by 144

Divide both sides of the equation by 144 to solve for h:

h = 324/144

h = 2.25

Therefore, the height of the cylinder is 2.25 inches.

Frequently Asked Questions (FAQs)

Q: What is the formula for the volume of a cylinder?

A: The formula for the volume of a cylinder is V = πr^2h.

Q: How do I calculate the height of a cylinder?

A: To calculate the height of a cylinder, use the formula V = πr^2h and plug in the values for the volume and radius. Then, solve for h.

Q: What is the radius of the base of the cylinder?

A: The radius of the base of the cylinder is the distance from the center of the base to the edge of the base.

Q: What is the height of the cylinder?

A: The height of the cylinder is the distance from the base of the cylinder to the top of the cylinder.

Q: How do I simplify the equation?

A: To simplify the equation, evaluate the expressions inside the parentheses and combine like terms.

Q: What is the value of π?

A: The value of π is approximately 3.14.

Conclusion

In conclusion, calculating the height of a cylinder involves using the formula V = πr^2h and plugging in the values for the volume and radius. By simplifying the equation and solving for h, we can find the height of the cylinder. Remember to use the correct formula and values to ensure accurate results.