Cylinder surface area

Surface Area of a Cylinder

Definition of Surface Area in a Cylinder

  • The surface area of a cylinder consists of:

    • Two circular bases (top and bottom)

    • A rectangular side that wraps around the circular bases

Surface Area Formula

  • The formula for the surface area (SA) of a cylinder is given by: SA = 2 ext{π}r^2 + 2 ext{π}rh where:

    • r = radius of the base of the cylinder

    • h = height of the cylinder

    • ext{π} (Pi) is approximately 3.14 (or the more precise value of rac{22}{7}, depending on the context of the problem)

Example Calculation

  • To find the surface area of a cylinder with:

    • Radius r = 5 cm

    • Height h = 10 cm

Step-by-Step Calculation

  1. Calculate the area of the two circles:

    • Use the formula for the area of a circle, which is ext{Area} = ext{π}r^2:

    • Area of one circle = ext{π}(5)^2 = 3.14 imes 25 = 78.5 cm²

    • Area of two circles = 2 imes 78.5 = 157 cm²

  2. Calculate the area of the rectangular side:

    • The area of the rectangle is given by the formula: ext{Area} = ext{circumference} imes h, where circumference of the base is 2 ext{π}r:

    • Circumference = 2 imes 3.14 imes 5 = 31.4 cm

    • Area of the rectangular side = 31.4 imes 10 = 314 cm²

  3. Add both areas together to find total surface area:

    • Total surface area = Area of two circles + Area of rectangle

    • Total surface area = 157 + 314 = 471 cm²

Conclusion

  • Therefore, the surface area of a cylinder with a radius of 5 cm and height of 10 cm is:
    471 ext{ cm}^2

Key Takeaways

  • The surface area of a cylinder can be found by combining the areas of its two circular bases and the rectangular side.

  • Understanding the formula is crucial for applying it to various problems and scenarios involving cylinders.