6. A large conference table is made from four rectangular sections and
four corner sections.
Each rectangular section is 4 m long and 1.2 m wide.
Each corner section is a quarter circle, radius 1.2 m.
Each person sitting at the conference table requires one metre of its
outside perimeter.
Calculate the greatest number of people who can sit around the
outside of the table.
Show all your working.
First, let's calculate the perimeter of each section:
Rectangular section:
Perimeter = 2(Length + Width)
Perimeter = 2(4m + 1.2m)
Perimeter = 2(5.2m)
Perimeter = 10.4m
Corner section:
Perimeter = 2πr/4
Perimeter = π(1.2m)/2
Perimeter = 1.2πm
Now, let's calculate the total perimeter of the table by adding up the perimeters of all sections:
Total perimeter = 4(10.4m) + 4(1.2πm)
Total perimeter = 41.6m + 4.8πm
Total perimeter ≈ 56.22m
Since each person requires 1m of the outside perimeter, the greatest number of people who can sit around the outside of the table is:
Number of people = Total perimeter / 1m
Number of people ≈ 56.22m / 1m
Number of people ≈ 56
Therefore, the greatest number of people who can sit around the outside of the table is 56.