Calculating Area Of A Circle With A Sector Removed

What is the area of a circle with a diameter of 2 ft after a sector of 60° has been removed?

Given:

           Diameter = 2 ft

Sector removed = 60°

What is asked:

Area of a circle after 60° has been removed

Solution:

1. Solving for radius.

              Radius = Diameter ÷ 2
                          = 2 ft ÷ 2
                          = 1 ft

2. Now this is the formula in getting the area of a circle.

Area of a circle = π r² × (360° - 60°)

                                            360°

                        = 3.1416 × (1 ft)²  × (360° - 60°)
                                                              360°
                        = 3.1416 × 1 ft² × (300°)
                                                      360°
                        = 3.1416 ft² × 0.83333
                        = 2.62 ft² is the area of a circle with 60 sector removed
                     

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Calculating Rope's Diameter

If the circumference of a mooring rope is 250 mm, what is the diameter?

Given:

Rope circumference = 250 mm

What is asked:

Diameter of a rope

Solution:

Circumference = π × Diameter

Circumference = π  ×Diameter 
          π                        π 
Circumference = Diameter
          π
          250 mm  = Diameter
          3.1416
             80 mm = Diameter 

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Calculate How Many Board Feet

You are to load a consignment of lumber. Each piece measure 3-inches thick, 12-inches wide and 16-feet long. There are 30,000 pieces in the shipment. How many board feet would be listed on the Bill of Lading?

Given:

Measurement of each stick: 3 in 12 in 16 ft
Total number of sticks = 30,000 pieces

What is asked:

Number of board feet

Solution:

One board feet is equal to 1 ft lenght × 1 ft width × 1 in height.

1. We have to calculate how many board feet in one stick.

      Board feet = L × W × H  
                                12
                       = 3 × 12 × 16 
                                 12
                       = 48 board feet in one stick

2. Since there are a total of 30,000 pieces of the same kind of stick, so

       30,000 sticks  ×  48 board feet  = 1,440,000 total board feet
                                  1 stick 

                 

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