Geometry Calculations: Circumference, Area, Surface Area, Volume

Circumference of Circles

• To find the circumference of a circle, use the formula:
  C = 2\pi r
  where $C$ is the circumference and $r$ is the radius.
• Round your answer to the nearest tenth.

Area of Circles

• The area of a circle is found using the formula:
  A = \pi r^2
  where $A$ is the area and $r$ is the radius.
• Round your answer to the nearest tenth.

Examples of Values:

1. Circle 1:
   • Radius = 9.1 inches
   • Circumference:
     • C = 2 \pi (9.1) \approx 57.2 \text{ in}
   • Area:
     • A = \pi (9.1)^2 \approx 260.4 \text{ in}^2
2. Circle 2:
   • Radius = 11 cm
   • Circumference:
     • C = 2 \pi (11) \approx 69.1 \text{ cm}
   • Area:
     • A = \pi (11)^2 \approx 380.1 \text{ cm}^2

Surface Area of Figures

• To find the surface area, use appropriate formulas depending on the shape:
  • Rectangular Prism:
    SA = 2(lw + lh + wh)
  • Cylinder:
    SA = 2\pi r(h + r)

Example of Surface Area Calculations:

1. Rectangular Prism:
   • Dimensions (length, width, height): 10 in, 5 in, 8 in
   • Surface Area:
     • SA = 2(10 \times 5 + 10 \times 8 + 5 \times 8) \approx 560 \text{ in}^2

Volume of Figures

• Volume formulas are specific to the figure:
  • Rectangular Prism:
    V = lwh
  • Cylinder:
    V = \pi r^2 h
• Round the answer to the nearest tenth.

Example of Volume Calculations:

1. Rectangular Prism:
   • Dimensions: 9 yd, 2 yd
   • Volume:
     • V = 9 \times 2 \times 11 \approx 198 \text{ yd}^3
2. Cylinder:
   • Height = 5.8 ft, Radius = 6 ft
   • Volume:
     • V = \pi (6)^2 (5.8) \approx 1097.2 \text{ ft}^3