Calculating the Volume of a Cylinder: Step-by-Step Guide with Example Calculation

Volume of a Cylinder Formula

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

V = πr^2h

Where:
V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3

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

V = πr^2h

Where:
V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3.14159
r is the radius of the cylinder
h is the height of the cylinder

To find the volume, we need to know the values of the radius and height of the cylinder. The radius is the distance from the center of the circular base to any point on the edge of the base, and the height is the perpendicular distance between the two bases.

Here’s how you can use the formula to calculate the volume of a cylinder:

1. Find the radius (r) and height (h) of the cylinder. Make sure that the units of measurement for both the radius and height are the same (e.g., centimeters, inches, etc.)

2. Calculate the area of the circular base by using the formula for the area of a circle: A = πr^2. Substitute the value of the radius (r) into this formula and solve for A.

3. Multiply the area of the base (A) by the height (h) of the cylinder: Volume (V) = A * h.

4. Substitute the value of A from step 2 into the formula: V = (πr^2) * h.

5. Calculate the value of V using the given values for r and h.

Remember to round the final answer to an appropriate number of significant figures based on the accuracy of the given values.

Let’s look at an example to understand this process:

Example: Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm.

Solution:
Given:
r = 5 cm
h = 10 cm

Step 1: Write down the given values.
r = 5 cm
h = 10 cm

Step 2: Calculate the area of the circular base.
A = πr^2
Substituting the value of r: A = π(5 cm)^2 = 25π cm^2

Step 3: Multiply the area of the base by the height.
V = A * h
Substituting the values of A and h: V = 25π cm^2 * 10 cm

Step 4: Simplify the expression.
V = 250π cm^3

Step 5: Calculate the final value using the approximation of pi.
V ≈ 250 * 3.14159 ≈ 785.398 cm^3

Therefore, the volume of the given cylinder is approximately 785.398 cm^3.

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