Surface Area of a Cylinder

Formula for Surface Area

• The surface area formula for a prism, which applies to cylinders due to their two congruent parallel circular bases, is:

  • Formula: (2B + PH)

    • Where:

      • (B) = base area

      • (P) = perimeter of the base

      • (H) = height (distance between the bases)

• For cylinders, the formula can be altered as:

  • Modified Formula: (2B + CH)

    • Here, (C) represents the circumference of the circular base instead of perimeter.

Calculating Areas and Circumference

Area of the Circular Base

• The formula to calculate the area of a circle is:

  • Area formula: (A = \pi r^2)

• For this example with radius (r = 6):

  • (A = \pi \times 6^2 = \pi \times 36 = 36\pi)

  • Hence, area for two bases: (2B = 2 \times 36\pi = 72\pi)

Circumference of the Circular Base

• The formula for circumference is:

  • Circumference formula: (C = 2\pi r)

• Substituting the radius:

  • (C = 2 \times \pi \times 6 = 12\pi)

Final Surface Area Calculation

• Now, plug in the values into the modified formula:

  • Surface Area: (2B + CH = 72\pi + 12\pi \times 10)

• Calculate:

  • (12\pi \times 10 = 120\pi)

• Combine like terms:

  • (72\pi + 120\pi = 192\pi)

Conclusion

• The final expression for the surface area of the cylinder is:

  • (192\pi) square feet.

• Remember the significance of (\pi) in your final answer to avoid losing accuracy.

• Approximately, (192\pi) equals 603 when squared and multiplied.