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 area formula for 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 smallest radius

The smallest radius \( r \) that the base can support is 6 inches.

Step3: Calculate smallest area

Substitute \( r = 6 \) into the area formula: \( A = \pi \times 6^2 = \pi \times 36 \approx 3.14159 \times 36 \approx 113.097 \). Rounding to the nearest whole number gives 113.

Largest Possible Area

Step1: Recall area formula for 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 largest radius

The largest radius \( r \) that the base can support is 23 inches.

Step3: Calculate largest area

Substitute \( r = 23 \) into the area formula: \( A = \pi \times 23^2 = \pi \times 529 \approx 3.14159 \times 529 \approx 1661.90 \). Rounding to the nearest whole number gives 1662.

Answer:

Smallest possible area: 113 square inches
Largest possible area: 1662 square inches