Surface Areas of Cylinders

Surface Areas of Cylinders

• Learning Target: Find the surface area of a cylinder.

• Success Criteria:
    - Use a formula for the surface area.
    - Determine lateral surface area.

• Key Concepts:   - A cylinder has two parallel identical circular bases.   - Surface area formula:
  $S = 2 ext{π}r^{2} + 2 ext{π}rh$
      - Where r = radius and h = height.   - Lateral surface area formula:
  $S = 2 ext{π}rh$

• Examples:
    1. Finding surface area:      - Example: For radius 4 and height 3:
  $S = 2 ext{π}(4)^{2} + 2 ext{π}(4)(3) = 56 ext{π}$        - Area = 176 square mm.   2. Finding lateral surface area:      - Example: For radius 4 and height 5:
  $S = 2 ext{π}(4)(5) = 40 ext{π} ext{ft}^{2} ext{(approx. 125.6 ft²)}$

• Real-Life Application:   - Calculate recycling returns based on surface area and weight of aluminum from cans.   - Example: For 24 cans with a surface area of 25.5π square inches, earnings can be calculated based on weight and per pound value of aluminum.

• Problem-Solving Plan:
    - Understand the problem, make a plan, solve, and check results.