Consider five circles with radii of 1, 2, 4, 8, and 16 inches. Write your answer in terms of \(\pi r^2\).
1. Compare the areas and circumferences of a circle when you double the radius.
- What happens to the area?
- What happens to the circumference?
2. What happens to the area when you triple the radius?
The table lists the radius, circumference, and area:
\[
\begin{array}{|c|c|c|}
\hline
\text{Radius (inches)} & \text{Circumference (inches)} & \text{Area (square inches)} \\
\hline
1 & 2\pi & \pi \\
2 & 4\pi & 4\pi \\
4 & 8\pi & 16\pi \\
8 & 16\pi & 64\pi \\
16 & 32\pi & 256\pi \\
\hline
\end{array}
\]
Answer (2)
Doubling the radius of a **circle quadruples **the area and doubles the circumference. Tripling the radius increases the area nine times and triples the circumference. ;
Doubling the radius of a circle quadruples the area and doubles the circumference. Tripling the radius increases the area nine times. The circumference triples when the radius is tripled.
;
