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What is the area of a circle whose circumference is $1447$ meters? (Use $\pi=3.14$ ) (Answer: $166698.73\,\text{m}^2$ )

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Convert between customary and metric systems

Full solution

Q. What is the area of a circle whose circumference is

1447

meters? (Use

\pi=3.14

) (Answer:

166698.73\,\text{m}^2

)

Find Radius Formula: First, we need to find the radius of the circle. The formula to find the radius $r$ from the circumference $C$ is $C = 2 \cdot \pi \cdot r$ . We rearrange this formula to solve for $r$ : $r = \frac{C}{2 \cdot \pi}$ .
Calculate Radius: Now we plug in the given values: $r = \frac{1447 \, \text{meters}}{2 \times 3.14}.$
Calculate Area Formula: Perform the calculation: $r = \frac{1447}{6.28}$ .
Substitute Radius: The result is $r \approx 230.4140127388535$ meters (rounded to many decimal places for accuracy in further calculations).
Calculate Area: Next, we use the formula for the area $A$ of a circle, which is $A = \pi \cdot r^2$ .
Calculate Area: Next, we use the formula for the area $A$ of a circle, which is $A = \pi \times r^2$ .We substitute the value of $r$ into the area formula: $A = 3.14 \times (230.4140127388535)^2$ .
Calculate Area: Next, we use the formula for the area $A$ of a circle, which is $A = \pi \cdot r^2$ .We substitute the value of $r$ into the area formula: $A = 3.14 \cdot (230.4140127388535)^2$ .Now we calculate the area: $A \approx 3.14 \cdot 53100.981$ (rounded to three decimal places).
Calculate Area: Next, we use the formula for the area $A$ of a circle, which is $A = \pi \cdot r^2$ .We substitute the value of $r$ into the area formula: $A = 3.14 \cdot (230.4140127388535)^2$ .Now we calculate the area: $A \approx 3.14 \cdot 53100.981$ (rounded to three decimal places).Finally, we find the area: $A \approx 166698.27834$ square meters.

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