Question

1. one circular table has a diameter of 9 ft, and another circular table has a diameter of 14 ft. how much greater is the area of the larger table? round to the nearest whole number.

about 108 ft²
about 72 ft²
about 90 ft²
about 36 ft²

Explanation:

Step1: Calculate radius of first table

Radius $r_1 = \frac{9}{2} = 4.5$ ft

Step2: Calculate area of first table

Area $A_1 = \pi r_1^2 = \pi (4.5)^2 ≈ 63.62$ ft²

Step3: Calculate radius of second table

Radius $r_2 = \frac{14}{2} = 7$ ft

Step4: Calculate area of second table

Area $A_2 = \pi r_2^2 = \pi (7)^2 ≈ 153.94$ ft²

Step5: Find area difference

Difference $= A_2 - A_1 ≈ 153.94 - 63.62 ≈ 90.32$ ft² (rounded to nearest whole number is 90, but wait—wait correction: Wait 14 diameter radius 7: π49≈153.94; 9 diameter radius 4.5: π20.25≈63.62; difference≈90.32≈90? Wait no wait the options: about 90 ft² is an option. Wait my mistake earlier—yes 90.32 rounds to 90. So the answer is about 90 ft².

Wait correction in steps:

Step1: Radius of smaller table

$r_1 = 9/2 = 4.5$ ft

Step2: Area of smaller table

$A_1 = π*(4.5)^2 ≈ 63.62$ ft²

Step3: Radius of larger table

$r_2 =14/2=7$ ft

Step4: Area of larger table

$A_2=π*(7)^2≈153.94$ ft²

Step5: Compute difference

$153.94 -63.62≈90.32≈90$ ft²

Final answer: about 90 ft²

Answer:

about 72 ft²