A dinner table is a perfect circle with a diameter of 8 feet With dinner plates that each have a diameter of exactly 1 foot, how much of the tablecloth will be showing when the table is set for six people ?

The area of the tablecloth showing is approximately 45.55 square feet

Step-by-step explanation:

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

The area of the tablecloth showing when the table is set for six people, A ≈ 45.55 ft.²

step-by-step explanation: