Answer:
- <em>The smallest possible are of the tabletop is </em><u>113 in²</u>
- <em>The largest possible area of the tabletop is </em><u>1,662 in²</u>
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) <u>Area of a circle: A = π r²</u>
The smallest area is given by the smallest radius, which we have just stated that is 6 in.
<u>b) Calculations:</u>
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.
<u>a) Area of a circle: A = π r²</u>
The largest area is given by the largest radius, which we have just stated that is 23 in.
<u>b) Calculations:</u>
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.
