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: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Calculate the smallest possible area

Given the smallest radius \(r = 6\) inches. Substitute \(r = 6\) into the formula:
\(A=\pi\times6^{2}=\pi\times36\approx3.14\times36 = 113.04\approx113\) square inches.

Step3: Calculate the largest possible area

Given the largest radius \(r = 23\) inches. Substitute \(r = 23\) into the formula:
\(A=\pi\times23^{2}=\pi\times529\approx3.14\times529 = 1661.06\approx1661\) square inches.

Answer:

113 square inches
1661 square inches