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:
     • $V = \pi (6)^2 (5.8) \approx 1097.2 \text{ ft}^3$