Question

The perimeter of a circle is 176 cm. Then Find the area of the circle.​

Answer 1

GIVEN :-

• Perimeter of the circle = 176 cm

TO FIND :-

• Area of the circle

SOLUTION :-

Perimeter of a circle is given by ,

$\\ \star \: \boxed{\purple{\sf{Perimeter = 2\pi r}}}$

Where ,

• r is radius

By substituting the values ,

$\\ : \implies \sf \: 176 \: cm = 2\pi r$

$\\ : \implies \sf \: 176 \: cm = 2 \times \frac{22}{7} \times r$

$\\ :\implies \sf \: 176 \: cm \times \frac{7}{2 \times 22} = r$

$\\ : \implies \sf \: 4 \times 7 \: cm = r$

$\\ : \implies{\boxed{\red{\mathfrak{r = 28 \: cm}}}}$

Now , Area of circle is given by ;

$\\ \star \:\boxed{\purple{\sf{Area \: = \pi {r}^{2} }}}$

$\\ : \implies \sf \:Area = \frac{22}{7} \times {(28)}^{2}$

$\\ : \implies \sf \: Area = \frac{22}{7} \times 784 \: cm {}^{2}$

$\\ : \implies{\boxed{\pink{\mathfrak{area = 2464 \: cm {}^{2} }}}} \: \bigstar$

$\\ \sf {\underline{Hence\:,\:The\:Area\:of\:the\:circle\:is\: \bold{2464\:cm^2}}}$

Answer 2

Solution

Given ,

• The perimeter of the circle = 176 cm

To find ,

• The area of the circle = ?

So ,

• Let the radius of a circle = r cm
• circumference of a circle = 2πr cm
• Diameter of a circle = 2r cm

Now ,

• Circumference of the circle + Diameter of the circle = 176cm

=> 2πr + 2r = 176

=> 2πr(π+1)=176

=> 2r = (3.14+1)=176

=> 2r × 4.14 = 176

=> r = 176 / 2×4.14

=> r = 21.26 cm

Now ,

• Area of circle = πr^2

Area of circle = 3.14 × 21.36 × 21.36

Area of circle = 1419.24 cm ^2

The area of circle is 1419.24cm^2 .