Question

the circumferences of three circular fountains are shown. the circles are not drawn to scale. circle h: $3sqrt{200}$ ft, circle m: $14pi$ ft, circle t: $43\frac{1}{2}$ ft. drag the shape names to appropriate boxes to list the circular fountains in order by their circumferences from greatest circumference to least circumference. greatest, least, :: circle h, :: circle t, :: circle m

Explanation:

Step1: Simplify the circumference of Circle H

First, simplify $3\sqrt{200}$. We know that $200 = 100\times2$, so $\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}$. Then $3\sqrt{200}=3\times10\sqrt{2}=30\sqrt{2}\approx30\times1.414 = 42.42$ ft.

Step2: Evaluate the circumference of Circle M

The circumference of Circle M is $14\pi$. Since $\pi\approx3.14$, then $14\pi\approx14\times3.14 = 43.96$ ft.

Step3: Analyze the circumference of Circle T

The circumference of Circle T is $43\frac{1}{2}=43.5$ ft.

Step4: Compare the values

Comparing the three - values: $43.96>43.5 > 42.42$, so $14\pi>43\frac{1}{2}>3\sqrt{200}$.

Answer:

Greatest: Circle M
Middle: Circle T
Least: Circle H