46 Jennifer painted a tabletop that is shaped like a circle. The circumference of the tabletop is \( 6 \pi \) feet. Which measurement is dosest to the area of the tabletop In square feet? F \( 18.84 \mathrm{ft}^{2} \) G \( 28.26 \mathrm{ft}^{2} \) H \( 37.68 \mathrm{ft}^{2} \) J \( 113.04 \mathrm{ft}^{2} \)

To find the area of the circular tabletop, we first need to determine its radius. The circumference \( C \) of a circle is given by the formula \( C = 2\pi r \). Given that \( C = 6\pi \) feet, we can set up the equation: \[ 6\pi = 2\pi r \] Dividing both sides by \( 2\pi \) gives us: \[ r = 3 \text{ feet} \] Now, we can calculate the area \( A \) using the formula \( A = \pi r^2 \): \[ A = \pi (3^2) = 9\pi \text{ square feet} \] Using the approximation \( \pi \approx 3.14 \): \[ A \approx 9 \times 3.14 \approx 28.26 \text{ square feet} \] So, the measurement closest to the area of the tabletop is **G \( 28.26 \text{ ft}^2 \)**! If you’re ever faced with calculating the area of a circle, remember: it's all about the radius — half the diameter — and using that cute little π! You’ll be impressing your friends with your circle skills in no time. Speaking of circles, did you know the ancient Greeks were the first to theoretically derive the value of π? They approximated it with various methods, but it was Archimedes who came up with a remarkable geometric approach, realizing it could be estimated by inscribing and circumscribing polygons around a circle! Math magic is timeless!