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Q.

[[1]] is the area of the quadrant of the circle whose circumference is 44 cm.

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Detailed Solution

Given, the circumference of the circle = 44 cm
We have to find the area of the quadrant of the circle.
seo

seo

Suppose the given circle has the circumference of 44 cm, so its quadrant area will be ABC. From the diagram, it is clear that the quadrant of the circle is

\frac{1}{4} th

of the circle so the area of quadrant will also be

\frac{1}{4} th

of the area of the circle.
First, we will find the radius of the circle using the formula of the circumference of the circle which is given as-
⇒ Circumference of the circle = 2πr where r is the radius of the circle
On putting the given values, we get-
⇒44 = 2πr
On rearranging, we get-

\Rightarrow \frac{44}{2 π} = r

On solving, we get-

\Rightarrow \frac{22}{π} = r

Now, we know that the area of the circle = πr2
So on putting the value of r, we get-
⇒ Area of the circle

= π \times \frac{22}{π} \times \frac{22}{π}

On solving, we get-
⇒ Area of the circle =

22 \times \frac{22}{π}

On putting the value of pi constant, we get-
⇒ Area of the circle =

22 \times \frac{22}{22} \times 7

On solving, we get-
⇒ Area of the circle=22×7cm2 -- (i)
Now, the area of the quadrant of the circle =

\frac{1}{4} th

of the area of the circle
So, we can write-
⇒Area of the quadrant of the circle =

\frac{22 \times 7}{4} c m^{2}

On solving, we get-
⇒Area of the quadrant of the circle

= \frac{11 \times 7}{2} = \frac{77}{2} c m^{2}

On further solving, we get-
⇒Area of the quadrant of the circle = 38.5 cm2

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