Question

Please answer this question with appropriate explanation . Please don't spam....

Answer 1

$\huge\green{Answer}$

If O is the centre of the circle, angle POQ = 90 degrees and the area of the shaded region is 126 cm² then the radius of a circle is 21 cm.

Step-by-step explanation:

It is given that,

∠POQ = θ = 90°

Area of shaded region = Area of the segment PRQ = 126 cm²

Let the radius of the circle be “r” cm

We know that the formula of the area of the segment is given by,

Area = \frac{r^2}{2}

$[{(πθ)/180} - sinθ]$

Substituting the given values in the formula, we get

126 = \frac{r^2}{2}

[{(π*90)/180} – sin90]

⇒ 252 = r² [(3.14/2) - 1]

⇒ 252 = r² * 0.57

⇒ r² = 442.10

⇒ r = 21.02 cm ≈ 21 cm

Thus, the radius of the circle is 21 cm.

Answer 2

If O is the centre of the circle, angle POQ = 90 degrees and the area of the shaded region is 126 cm² then the radius of a circle is 21 cm.

It is given that,

∠POQ = θ = 90°

Area of shaded region = Area of the segment PRQ = 126 cm²

Let the radius of the circle be “r” cm

We know that the formula of the area of the segment is given by,

Area = \frac{r^2}{2}

$[{(πθ)/180} - sinθ][(πθ)/180−sinθ]$

Substituting the given values in the formula, we get

126 = \frac{r^2}{2}

$[{(π*90)/180} – sin90]$

⇒ 252 = r² [(3.14/2) - 1]

⇒ 252 = r² * 0.57

⇒ r² = 442.10

⇒ r = 21.02 cm ≈ 21 cm

Thus, the radius of the circle is 21 cm.