Question

The perimeter of circular field is 242 m . the area is?
(1 Point)
9317 sq.m
18634 sq.m
4658.5 sq.m
none of these
​

Answer 1

Given: Perimeter (Circumference) of circular field is 242 m

To find: Area of circular field?

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We know that,

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$\star\;{\boxed{\sf{\purple{Perimeter_{\;(circle)} = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 242\\ \\ :\implies\sf \dfrac{44}{7} \times r = 242\\ \\ :\implies\sf r = \cancel{242} \times \dfrac{7}{ \cancel{44}}\\ \\ :\implies\sf r = 5.5 \times 7\\ \\ :\implies{\boxed{\sf{\pink{r = 38.5\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Radius\;of\; circular\;field\;is\; {\textsf{\textbf{8.5\;cm}}}.}}}$

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Area of circular field,

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$\star\;{\boxed{\sf{\purple{Area_{\;(circle)} = \pi r^2}}}}$

$:\implies\sf Area_{\;(field)} = \dfrac{22}{7} \times (38.5)^2\\ \\ :\implies\sf Area_{\;(field)} = \dfrac{22}{7} \times 38.5 \times 38.5\\ \\ :\implies{\boxed{\sf{\pink{Area_{\;(field)} = 4658.5\;cm^2\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\; circular\;field\;is\; \bf{4658.5\;cm^2}.}}}$

Answer 2

Answer:

Given :-

• The perimeter of a circular field is 242 m.

To Find :-

• What is the area of a circular field.

Solution :-

Perimeter of a circular field is 242 m.

According to the question by using the formula we get,

❖ Perimeter = 2πr

⇒ 242 = 2 × $\dfrac{22}{7}$ × r

⇒ 242 = $\dfrac{44}{7}$ × r

⇒ $\dfrac{44}{7}$ × r = 242

⇒ r = 242 × $\dfrac{7}{44}$

⇒ r = 38.5 cm

Now, we have to find the area of circular field,

❖ Area = πr²

⇒ Area = $\dfrac{22}{7}$ × (38.5)²

⇒ Area = $\dfrac{22}{7}$ × $\dfrac{385}{10}$ × $\dfrac{385}{10}$

➠ Area = 4658.5 cm²

$\therefore$ The area of a circular field is 4658.5 cm² .