Question

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

Answer 1

Solutions :-

Given :
Area of circle = Area of rectangle
Length of Rectangle = 112 m
Breadth = 88 m


Find the radius of circle :-

We know that,
Area of circle = Area of rectangle
=> πr² = (Length × Breadth)
=> πr² = (112 × 88)
=> πr² = 9856
=> r² = 9856/π
=> r² = 3136
=> r = √3136 = 56


Now,
Find the circumference of the circle :-

Circumference of circle = 2πr
= 2 × 22/7 × 56
= 2 × 22 × 8
= 352 m


Hence,
Circumference of circle = 352 m

Answer 2

ANS :

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Length of the rectangle =112m

Breadth of the rectangle =88m

Also,
Area of the circle =Area of the rectangle i.e,

$\pi {r}^{2} = l \times b(where \: l = length \: and \: b = breadth)$

As we know the formula for circumference of the circle is 2πr.

So we first need to find the radius of the circle.

As mentioned in the question,

Area of the circle =Area of the rectangle,

$\pi {r}^{2} = (length \times breadth) \\ \pi {r}^{2} = (112m \times 88m)........given \:length \: and \: breadth \: in \: the \: question \: \\ \pi {r}^{2} =9856 \\ {r}^{2} = \frac{9856}{ \frac{22}{7} }(taking \: value \: of \: \pi = \frac{22}{7}) \\ {r}^{2} = 3,136 \\ \sqrt{ {r}^{2} } = \sqrt{3136}(taking \: square \: roots \:on \: both \: sides) \\ r = 56$
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Now as we have the radius of our circle we can now get the circumference of the circle using the formula,

C=2πr(Where,C=Circumference and r=radius)

$c = 2 \times \frac{22}{7} \times 56 \\ c = 2 \times 22 \times 8(dividing \: 56 \: by \: 7) \\ c = 352m$
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THEREFORE,
CIRCUMFERENCE OF THE CIRCLE=352 m

RADIUS OF THE CIRCLE=56m
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