The area of the tablecloth showing is approximately 45.55 square feet
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called as the area of the circle.
It is given that:-
The diameter of the dinner table, D = 8 feet
The diameter of each plate, d = 1 feet
The number of people at the dinner table = 6 people
The number of plates = 6 plates
The area of the table cloth, A₁ = π·D²/4
∴ A₁ = π × 8²/4
The area covered by the 6 plates, A₂ = 6·π·d²/4
A₂ = 6 × π × 1²/4
Let 'A' represent the area of the tablecloth showing when the table is set for six people, we have;
A = A₁ - A₂
∴ A = π × 8²/4 - 6 × π × 1²/4 ≈ 45.55 ft.²
Therefore the area of the tablecloth showing when the table is set for six people, A ≈ 45.55 ft.²
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