Question

Please help me out of this questions

Answer 1

☆ ANSWER:

Your Answer is 41.04 cm²

☆ Explanation:

Given:-

• Radius of the circle = 6cm.

To Find:-

• The area of shded region.

Formulas Used:-

$\\ 1. \: \tt d = \sqrt{2}s. \\ \\ 2. \: \tt \: area \: of \: circle \: = \pi {r}^{2}. \\ \\ 3. \:\tt area \: of \: square = (s) {}^{2}.$

Where,

• d = Diagonal of a square.

• s = Side of the square.

• $\pi$ = 3.14

• r = Radius of the circle.

So Here,

Area of shaded region

= Area of circle - Area of square.

And also to find the area of square we have to first find out the side of that square.

$\because$ In the given figure,

Diameter of the circle = Diagonal of the square.

Also, Diameter = 2 × radius.

$\implies$ Diameter = 2 × 6cm.

$\implies$ Diameter = 12cm = Diagonal.

Also,

We know that,

$\tt\mapsto \: d = \sqrt{2} \times s \\ \\ \tt\mapsto \: 12cm = \sqrt{2} s. \\ \\ \tt\mapsto(12cm) {}^{2} = ( \sqrt{2} s) {}^{2} \\ \\ \sf(squaring \: both \: sides) \\ \\ \tt\mapsto144cm {}^{2} = 2 {s}^{2} \\ \\ \tt\mapsto {s}^{2} = \frac{\cancel{144cm} {}^{2} }{\cancel{2}} \\ \\ \tt\mapsto {s}^{2} = 72 {cm}^{2} .$

So we have got the value of s² = 72 cm²..(1)

Also area of square = s²..(2)

So From (1) and (2) we get,

Area of square = 72 cm².

Again,

Area of circle = $\pi r^2$

$\sf = 3.14 \times (6cm) {}^{2} \\ \\ \sf = 3.14 \times 36 \: cm {}^{2} \\ \\ \sf = 113.04 \: cm {}^{2}$

$\therefore$ Area of circle = 113.04 cm².

Therefore,

Area of shaded region,

= 113.04 cm² - 72 cm²

= 41.04 cm²