Question

the circumference of a circle is 42.7 metre find the diameter and area .
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Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bf{Given:-}\begin{cases}\sf{Circumference\:of\: circle=42.7m}\end{cases}$

$\huge\star{\sf{\red{To\:Find:-}}}$

• We have to find the area and the diameter of circle

$\bf\underline{\underline{\red{According\:to\: Question:-}}}$

$\boxed{\sf{\star{Circumference\:of\:circle=2\pi r }}}$

• Now find the radius of circle

$\sf\implies 2\pi r=42.7\\ \\ \sf\implies 2\times \frac{22}{7}\times r=42.7\\ \\ \sf\implies 44r=42.7\times 7\\ \\ \sf\implies r=\frac{42.7\times 7}{44}\\ \\ \sf\implies r=\cancel{\frac{298.9}{44}}=6.79\\ \\ \sf\implies {\red{ radius=6.79m}}$

• The radius is 6.79m then the diameter of circle is 2r
• 2×6.79
• =>13.58cm

$\boxed{\star{\sf{Diameter=13.58m}}}$

• Now the area of circle

$\boxed{\sf{Area\:of\: circle=\pi r{}^{2}}}$

$\sf\implies Area\:of\:circle=\frac{22}{7}\times (6.79m){}^{2}\\ \\ \sf\implies Area\:of\: circle \frac{22\times 46.1041}{7}\\ \\ \sf\implies Area\:of\: circle=\cancel{\frac{1014.2902}{7}}=144.8986\\ \\ \sf\implies {\blue{Area\:of\: circle=144.8986m{}^{2}}}$

$\boxed{\star{\sf{Area\:of\: circle=144.8986m{}^{2}}}}$