What is the volume of a right circular cylinder of base radius 7 cm and height 10cm?

The exact volume of a right circular cylinder with a base radius of 7 cm and a height of 10 cm is 1540 cm³.

Understanding Cylinder Volume

A right circular cylinder is a three-dimensional shape with two parallel circular bases of the same size and a curved surface connecting them. The height is the perpendicular distance between the bases, and the radius is the radius of the circular base.

The volume of any cylinder is calculated using the formula:

Volume (V) = Area of the Base × Height

Since the base is a circle, its area is given by πr², where 'r' is the radius. Therefore, the formula for the volume of a right circular cylinder is:

V = πr²h

Where:

• V is the volume
• π (Pi) is a mathematical constant, approximately 3.14159 or commonly approximated as 22/7 for calculations involving multiples of 7
• r is the radius of the base
• h is the height of the cylinder

Calculating the Volume

To find the volume of the cylinder with a radius of 7 cm and a height of 10 cm, we plug these values into the formula. It is common to use the approximation π ≈ 22/7 when the radius is a multiple of 7, as it simplifies the calculation.

• Given:

  • Radius (r) = 7 cm
  • Height (h) = 10 cm
  • Using π ≈ 22/7

• Calculation Steps:

  1. Square the radius: r² = (7 cm)² = 49 cm²
  2. Multiply the base area (πr²) by the height (h):
     V = (22/7) × (49 cm²) × (10 cm)
  3. Simplify the multiplication:
     V = 22 × (49/7) cm² × 10 cm
     V = 22 × 7 cm² × 10 cm
     V = 154 cm² × 10 cm
     V = 1540 cm³

∴ The volume of a cylinder is 1540 cm3. This confirms the volume based on the given dimensions.

Here's a summary of the inputs and result:

Key Takeaways

• The volume of a cylinder depends directly on the square of its radius and its height.
• A slight change in the radius has a larger impact on the volume than a similar change in height.
• Units are crucial: when radius and height are in cm, the volume is in cm³.