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. 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.

Explanation:

1) What is the smallest possible area of the tabletop that will fit on Timothy’s table base?

The statement that the base can support a tabletop with a radius of at least 6 inches means that the radius has to be 6 inches or more, i.e. the smallest possible radius is 6 inches.

a) Area of a circle: A = π r²

The smallest area is given by the smallest radius, which we have just stated that is 6 in.

b) Calculations:

With that A = π (6 in)² = 36π in² ≈ 113.10 in².

Round the answer to the nearest whole square inch: 113 in²

2) What is the largest possible area of the tabletop that will fit on Timothy’s table base?

The statement that the base can support a tabletop with a radius no more than 23 inches means that the radius has to be 23 inches or less, i.e. the largest possible radius is 23 inches.

a) Area of a circle: A = π r²

The largest area is given by the largest radius, which we have just stated that is 23 in.

b) Calculations:

With that A = π (23 in)² = 529 π in² ≈ 1,661.9 in².

Round the answer to the nearest whole square inch: 1,662 in².