Question

3. A circle of area 314 cmis inscribed in a square. What is the perimeter of the square? (n=3.14) 1 ( (1) 28 cm (2) 40 cm (3) 80 cm (4) 100 cm .​

Answer 1

Answer:

Given :-

• A circle of area is 314 cm² is inscribed in a square.

To Find :-

• What is the perimeter of the square.

Solution :-

First, we have to find the radius of a circle :

Given :

• Area of circle = 314 cm²

As we know that :

$\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Circle)} =\: {\pi}r^2}}}\: \: \: \bigstar$

According to the question by using the formula we get,

$\implies \bf {\pi}r^2 =\: 314$

$\implies \sf \dfrac{22}{7} \times r^2 =\: 314$

$\implies \sf r^2 =\: 314 \times \dfrac{7}{22}$

$\implies \sf r^2 =\: \dfrac{2198}{22}$

$\implies \sf r^2 =\: 99.9$

$\implies \sf r^2 \approx 100(approx)$

$\implies \sf r^2 =\: 100$

$\implies \sf r =\: \sqrt{100}$

$\implies \sf\bold{\purple{r =\: 10}}$

Hence, the diameter of a circle is :

$\bigstar \: \: \sf\boxed{\bold{\pink{Diameter =\: 2 \times Radius}}}\: \: \: \bigstar$

$\implies \sf Diameter =\: 2 \times 10$

$\implies \sf\bold{\blue{Diameter =\: 20\: cm}}$

Again,

$\clubsuit \: \: \bf Side_{(Square)} =\: Diameter_{(Circle)}$

$\implies \sf Side_{(Square)} =\: 20\: cm$

Now, we have to find the perimeter of square :

As we know that :

$\bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Square)} =\: 4 \times Side}}}\: \: \: \bigstar$

Given :

• Side of Square = 20 cm

According to the question by using the formula we get,

$\dashrightarrow \sf Perimeter_{(Square)} =\: 4 \times 20\: cm$

$\dashrightarrow \sf\bold{\red{Perimeter_{(Square)} =\: 80\: cm}}$

$\therefore$ The perimeter of the square is 80 cm .

Hence, the correct options is option no (3) 80 cm .

Answer 2

Step-by-step explanation:

Answer:

Given :-

A circle of area is 314 cm² is inscribed in a square.

To Find :-

What is the perimeter of the square.

Solution :-

First, we have to find the radius of a circle :

Given :

Area of circle = 314 cm²

As we know that :

\begin{gathered}\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Circle)} =\: {\pi}r^2}}}\: \: \: \bigstar\\\end{gathered}★Area(Circle)=πr2★

According to the question by using the formula we get,

\implies \bf {\pi}r^2 =\: 314⟹πr2=314

\implies \sf \dfrac{22}{7} \times r^2 =\: 314⟹722×r2=314

\implies \sf r^2 =\: 314 \times \dfrac{7}{22}⟹r2=314×227

\implies \sf r^2 =\: \dfrac{2198}{22}⟹r2=222198

\implies \sf r^2 =\: 99.9⟹r2=99.9

\implies \sf r^2 \approx 100(approx)⟹r2≈100(approx)

\implies \sf r^2 =\: 100⟹r2=100

\implies \sf r =\: \sqrt{100}⟹r=100

\implies \sf\bold{\purple{r =\: 10}}⟹r=10

Hence, the diameter of a circle is :

\begin{gathered}\bigstar \: \: \sf\boxed{\bold{\pink{Diameter =\: 2 \times Radius}}}\: \: \: \bigstar\\\end{gathered}★Diameter=2×Radius★

\implies \sf Diameter =\: 2 \times 10⟹Diameter=2×10

\implies \sf\bold{\blue{Diameter =\: 20\: cm}}⟹Diameter=20cm

Again,

\clubsuit \: \: \bf Side_{(Square)} =\: Diameter_{(Circle)}♣Side(Square)=Diameter(Circle)

\implies \sf Side_{(Square)} =\: 20\: cm⟹Side(Square)=20cm

Now, we have to find the perimeter of square :

As we know that :

\begin{gathered}\bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Square)} =\: 4 \times Side}}}\: \: \: \bigstar\\\end{gathered}★Perimeter(Square)=4×Side★

Given :

Side of Square = 20 cm

According to the question by using the formula we get,

\begin{gathered}\dashrightarrow \sf Perimeter_{(Square)} =\: 4 \times 20\: cm\\\end{gathered}⇢Perimeter(Square)=4×20cm

\dashrightarrow \sf\bold{\red{Perimeter_{(Square)} =\: 80\: cm}}⇢Perimeter(Square)=80cm

\therefore∴ The perimeter of the square is 80 cm .

Hence, the correct options is option no (3) 80 cm .