Question

Area of a circle is 2464 cm² . Find its radius and circumference.

Answer 1

$\huge\sf\purple{{\underline{Answer}}:}$

$\sf{ }$

$\large\bf{{\underline{Given}}:}$

$\sf Area \: of \: the \: circle = 2464cm^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies \pi {r}^{2} = 2464 {cm}^{2} \\ \: \sf \implies \frac{22}{7} \times {r}^{2} = 2464 \\ \: \: \: \: \: \: \: \: \sf \implies 22 \times {r}^{2} = 7 \times 2464 \\ \: \: \sf \implies 22 \times {r}^{2} = 17248 \\ \sf \implies {r}^{2} = \frac{17248}{22} \: \: \: \: \: \: \: \\ \sf \implies {r}^{2} = 784 \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies r = \purple{ \underline{ \boxed{ \bf 28cm}}} \: \: \: \: \: \:$

$\large\bf\therefore{{\underline{Circumference~of~the~circle}}:}$

$\sf 2 \pi r \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies 2 \times \frac{22}{ \cancel{ \: 7} \: \: ^{1} } + { \cancel{28}} \: \: ^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies 2 \times 22 \times 4 \\ \sf \implies 44 \times 4 \: \: \: \: \: \: \: \\ \sf \implies \purple{ \underline{ \boxed{ \bf 176cm}}} \: \:$

$\sf{ }$

$\large\bf\therefore{{\underline{Required~answer}}:}$

$\sf Radius = \purple{ \underline{ \boxed{ \bf 28cm}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Circumference = \purple{ \underline{ \boxed{ \bf 176cm}}}$

Answer 2

Answer:

• Radius is 28cm.
• Circumference is 176cm. ✔

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Step-by-step explanation:

Given that,

• Area of a circle is 2464cm²

Here, the area is given we need to find it's radius and circumstance.

Step 1 :

We know that,

→ Area of a circle = πr²

• But, area is 2464cm² (given)
• Taking ‘π’ as 22/7
• ‘r’ is the radius.

So,

→ 2464 = 22/7 × r²

→ 2464 · 7/22 = r²

→ 112 · 7 = r²

→ 784 = r²

→ √784 = r

→ 28 = r

∴ The radius is 28 cm.

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Step 2 :

Finding it's circumstance :

Circumstance of a circle is given by :

→ 2πr

→ 2 · 22/7 · 28

→ 2 · 22 · 4

→ 176cm.

∴ The circumstance of the circle is 176 cm ✔

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