Answer:
- The minimum area for the tabletop is 113 in²
- The maximum area for the tabletop is 1,662 in²
Explanation:
1) What is the least area required for a tabletop that fits Timothy’s base?
The requirement that the base can accommodate a tabletop with a radius of at least 6 inches indicates that the smallest permissible radius is 6 inches.
a) Area of a circle is calculated as: A = π r²
The smallest area is determined by this minimum radius of 6 in.
b) Calculations:
Thus, A = π (6 in)² = 36π in² ≈ 113.10 in².
Rounding to the nearest whole square inch gives: 113 in²
2) What is the maximum area permitted for a tabletop on Timothy’s base?
The fact that the base can support a tabletop with a maximum radius of 23 inches indicates that the largest allowable radius is 23 inches.
a) Area of a circle is given by: A = π r²
The largest area corresponds to a radius of 23 in, as mentioned above.
b) Calculations:
Therefore, A = π (23 in)² = 529 π in² ≈ 1,661.9 in².
Rounding this result yields: 1,662 in².
