Question

timothy built a base for a circular tabletop. the base can support a tabletop with a radius of at least 6 inches, but not more than 23 inches.
what is the smallest possible area of the tabletop that will fit on timothys table base? round the answer to the nearest whole square inch.
square inches
what is the largest possible area of the tabletop that will fit on timothys table base? round the answer to the nearest whole square inch.
square inches

Explanation:

Step1: Use area formula for circle

The area of a circle is given by $A = \pi r^2$, where $r$ is the radius.

Step2: Calculate smallest area (r=6)

Substitute $r=6$ into the formula:
$A = \pi (6)^2 = 36\pi \approx 36 \times 3.1416 = 113.0976$
Round to the nearest whole number.

Step3: Calculate largest area (r=23)

Substitute $r=23$ into the formula:
$A = \pi (23)^2 = 529\pi \approx 529 \times 3.1416 = 1661.9064$
Round to the nearest whole number.

Answer:

113 square inches
1662 square inches