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A sumo wrestling ring is circular and has a circumference of
4.6 pi meters.
What is the area
A of the sumo wrestling ring in square meters? Give your answer in terms of
pi.

A sumo wrestling ring is circular and has a circumference of $4.6 \pi$ meters. $\newline$ What is the area $A$ of the sumo wrestling ring in square meters? Give your answer in terms of $\pi$ . $\newline$ $A=\square$ $\mathrm{m}^{2}$

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Area and perimeter: word problems

Full solution

Q. A sumo wrestling ring is circular and has a circumference of

4.6 \pi

meters.

\newline

What is the area

A

of the sumo wrestling ring in square meters? Give your answer in terms of

\pi

.

\newline

A=\square

\mathrm{m}^{2}

Circle Circumference Formula: The circumference $C$ of a circle is given by the formula $C = 2 \times \pi \times r$ , where $r$ is the radius.
Calculate Radius: Given the circumference is $4.6 \pi$ meters, we can set up the equation $4.6 \pi = 2 \times \pi \times r$ to find the radius.
Circle Area Formula: Divide both sides by $2 \pi$ to solve for $r$ : $r = \frac{4.6 \pi}{2 \pi} = 2.3$ meters.
Substitute Radius: The area $A$ of a circle is given by the formula $A = \pi \cdot r^2$ .
Calculate Area: Substitute $r = 2.3$ meters into the area formula: $A = \pi \times (2.3)^2$ .
Calculate Area: Substitute $r = 2.3$ meters into the area formula: $A = \pi \times (2.3)^2$ .Calculate the area: $A = \pi \times 5.29$ square meters.

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