Question

Find the area of a quadrant of a circle whose circumference is 44 cm.​

Answer 1

Given,

$\sf{Circumference\:of\:the\:circle\:is\:44\:cm}$

To find,

$\sf{Area\:of\:quadrant}$

Solution,

It should be noted that a quadrant of a circle is a sector which is making an angle of 90°

$\sf{Let\:the\:radios\:of\:the\:circle\:be\:r}$

• As,

$\large{\sf{C=2πr=44}}$

$\large\sf{⇒R=\frac{44}{2π}\:cm}$

$\large\sf{⇒ R=7\:cm}$

• So,

$\bf{Area\:of\:the\:quadrant,}$

$\sf{= \frac{θ}{360°} ×πr^2}$

Here, θ = 90°

• So,

$\sf\large{A=\frac{90°}{360°}×πr^2\:cm^2}$

$\sf\large{=\frac{1}{4}×π (7)^2\:cm^2}$

$\sf\large{=\frac{1}{4}×π×7×7\:cm^2}$

$\sf\large{=\frac{1}{4}×\frac{22}{7}×7×7\:cm^2}$

$\sf\large{=\frac{77}{2}\:cm^2}$

$\sf\large{=38.5\:\:cm^2}$

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$\large{ \underline{ \overline{ \mid{ \rm{ \red{Answer→38.5\:\:cm^2}} \mid}}}}$

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Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

It should be noted that a quadrant of a circle is a sector which is making an angle of 90°

Let the radios of the circle be r

As,

C=2πr=44

R= 44/2π cm

R= 7cm

So,

Area of the quadrant,

= θ/360° × πr²

Here, θ = 90°

So,

A= 90°/360° ×πr²cm²

= 1/4 ×π(7)² cm²

= 1/4 ×π×7×7cm²

= 1/4 × 22/7 ×7×7cm²

= 77/2 cm²

= 38.5cm²

AnSweR → 38.5cm²