Question

the area of a circle is equal to the area of a rectangle with sides 112 and 88 m. Find the circumference of the circle.

Answer 1

112 + 88 = 200 

A = πr^2 = 200 
r^2 = 200/π 
r = 10√(2/π) 

C = 2πr = 2π • 10√(2/π) = 20√(2π) m

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

$\textbf{\underline{Area\;of\;circle\;is\;equal\;to\;the\; Area\;of\;rectangle}}$

Also,

$\textbf{\underline{Length\;of\;rectangle\;(L)}}$

= 112 m

$\textbf{\underline{Breadth\;of\;rectangle\;(B)}}$

= 88 m

We know that :-

$\textbf{\underline{Area\;of\;rectangle}}$

= Length × Breadth

= 112 × 88

= 9856 m²

${\boxed{\sf\:{Also\;it\;is\;Given\;that :-}}}$

Area of circle = 9856 cm²

$\textbf{\underline{Using\;Formula :- }}$

πr² = 9856

$\tt{\rightarrow\dfrac{22}{7}\times r^2=9856}$

$\tt{\rightarrow r^2=9856\times\dfrac{7}{22}}$

r² = 3136

r = √(3136)

r = 56 m

$\textbf{\underline{Also\;here\;we\;know\;that,}}$

Circumference of circle = 2πr

$\tt{\rightarrow 2\times\dfrac{22}{7}\times 56}$

= 44 × 8

= 352 m

$\textbf{\underline{Therefore\;we\;get,}}$

$\Large{\boxed{\sf\:{Circumference\;of\;circle = 352 m}}}$