Question

Find the area and circumference of a circle whose radius is 10.5 cm (Take pi = 22/7)

Answer 1

Given :

• Radius of the circle is 10.5m.

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To find :

• circumference and Area of Circle?

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Solution :

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We know that,

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

Putting values,

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$:\implies\sf 2 \times \dfrac{22}{7} \times 10.5$

$:\implies\sf 44\times 1.5$

$:\implies{\boxed{\sf{\pink{ 66\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Circumference \;of\;circle\;is\; \bf{66\;cm}.}}}$

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Now, Finding area of Circle,

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

$:\implies\sf \dfrac{22}{\cancel{7}} \times \cancel{10.5} \times 7$

$:\implies\sf 22\times 15.75$

$:\implies{\boxed{\sf{\pink{346.5\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\;circle\;is\; \bf{346.5\;cm^2}.}}}$

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$\boxed{\underline{\underline{\bigstar \: \bf\:Formula\:Related\:to\:Circle\:\bigstar}}}$

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$\sf (i)\;Circumference \:of\;a\;circle\; = \; \red{2 \pi r}$

$\sf (ii)\;Area\:of\;a\;circle\; = \; \pink{\pi r^2}$⠀⠀⠀⠀⠀⠀⠀

$\sf (iii)\;Length \:of\;an\;arc\;of\;a\;sector\:of\;a\;circle\;with\;radius\:r\:and\:angle\:with\:degree\;measure's \: {\theta}\:is\; = \; \green{ \dfrac{ \theta}{360^\circ} \times 2 \pi r}$

$\sf (iv)\;Area\:of\;a\;sector\; = \; \purple{ \dfrac{ \theta}{360^\circ} \times \pi r^2}$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer 2

Given:-

⌬ Radius of circle = 10.5 cm.

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To find:-

⌬ Area and Circumference of circle.

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Solution:-

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★ Formula used

$\tt\longrightarrow{}$ $\boxed{\sf{\orange{Area~ of~ Circle = \pi r^2}}}$

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$\large{\tt{\longmapsto{Area = \pi r^2}}}$

$\large{\tt{\longmapsto{\dfrac{22}{7}\times 10.5\times 10.5}}}$

$\large{\tt{\longmapsto{22\times 1.5\times 10.5}}}$

$\large{\tt{\longmapsto{346.5 cm^2}}}$

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★ Formula used

$\tt\longrightarrow{}$ $\boxed{\sf{\purple{Circumference~ of~ Circle = 2\pi r}}}$

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$\large{\tt{\longmapsto{Circumference = 2\pi r}}}$

$\large{\tt{\longmapsto{2\times \dfrac{22}{7}\times 10.5}}}$

$\large{\tt{\longmapsto{2\times 22\times 1.5}}}$

$\large{\tt{\longmapsto{66 cm}}}$

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Hence,

• Area of circle = 346.5 cm²
• Circumference of circle = 66 cm

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