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 timothy’s 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 timothy’s table base? round the answer to the nearest whole square inch.

square inches

Explanation:

Smallest Possible Area

Step1: Recall the formula for the area of a circle

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

Step2: Identify the smallest radius

The base can support a tabletop with a radius of at least 6 inches. So, the smallest radius \( r \) is 6 inches.

Step3: Calculate the smallest area

Substitute \( r = 6 \) into the area formula: \( A = \pi (6)^2 = 36\pi \).
Now, calculate the numerical value: \( 36\pi \approx 36\times3.1416 \approx 113.1 \). Rounding to the nearest whole number gives 113.

Largest Possible Area

Step1: Recall the formula for the area of a circle

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

Step2: Identify the largest radius

The base can support a tabletop with a radius of not more than 23 inches. So, the largest radius \( r \) is 23 inches.

Step3: Calculate the largest area

Substitute \( r = 23 \) into the area formula: \( A = \pi (23)^2 = 529\pi \).
Now, calculate the numerical value: \( 529\pi \approx 529\times3.1416 \approx 1662.5 \). Rounding to the nearest whole number gives 1663.

Answer:

Smallest possible area: 113 square inches
Largest possible area: 1663 square inches