How can we calculate the volume of a cylinder expressed in terms of pi?

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Calculating the Volume of a Cylinder

To find the volume of a cylinder, we need to use a specific formula. The volume (V) of a cylinder can be calculated using the following equation:

V = πr2h

where:

  • V is the volume of the cylinder
  • r is the radius of the base of the cylinder
  • h is the height of the cylinder
  • π (pi) is a mathematical constant approximately equal to 3.14, but in this case, we will leave it in terms of pi.

### Step-by-Step Example:

  1. Identify the Radius and Height: Assume you have a cylinder with a radius of 3 units and a height of 5 units.
  2. Plug into the Formula: Substitute the values into the volume formula:
    3. V = π(3)2(5)
  3. Calculate: First, calculate the area of the base:
    4. (3)2 = 9
  4. Then multiply by the height:
    5. 9 * 5 = 45
  5. Now, combine it with pi:
    6. V = 45π

Thus, the volume of the cylinder in terms of pi is 45π cubic units. This formula is quite useful for calculating volumes in geometry and is applicable in various practical scenarios, including engineering and architecture.

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