Final answer:
Sylvia's tablecloth will fit on tables (c) and (d) because their calculated areas (314.16 in2 each) are the only ones that are close to the tablecloth's given area (254.34 in2) without being too small. The area of table (a) and table (b) are too small to fit the tablecloth.
Step-by-step explanation:
To determine which table Sylvia can place her circular tablecloth on, we must compare the surface area of the tables with the area of the tablecloth, which is 254.34 in2. To do this, we use the area formula for a circle, A = πr2, where A is the area and r is the radius of the circle.
- For table (a) with an 8-inch radius, the area is A = π × (8 in)2.
- For table (b) with a 14-inch diameter, the radius is 7 inches, so the area is A = π × (7 in)2.
- For table (c) with a 10-inch radius, the area is A = π × (10 in)2.
- For table (d) with a 20-inch diameter, the radius is 10 inches, so the area is also A = π × (10 in)2.
The only table sizes that match or exceed the given tablecloth's area of 254.34 in2 without going over will be suitable. Therefore, we calculate:
- For table (a), A = π × 82 = 64π in2
- For table (b), A = π × 72 = 49π in2
- For table (c), A = π × 102 = 100π in2
- For table (d), A = π × 102 = 100π in2
Approximating π ≈ 3.14, we find:
- For table (a), A ≈ 201.06 in2
- For table (b), A ≈ 153.86 in2
- For tables (c) and (d), A ≈ 314.16 in2
Therefore, the tablecloth will fit on tables (c) and (d) since their areas are closest to the provided tablecloth's area while not being too small.