Question

find the area of a circle whose circumference is 52.8.​

Answer 1

$\huge\boxed{Answer}$

We know that

Circumference of the circle = 2πr

52.8 = 2 × 22/7 × r

26.4 = 22/7 × r

r = 26.4 × 7/22

r = 1.2 × 7

r = 8.4 unit

Now ,

Area of the circle

= πr²

= 22/7 × 8.4 × 8.4

= 22/7 × 42/5 × 42/5

= (22 × 42 × 42) / (7 × 5 × 5)

= (22 × 6 × 42) / 25

= 22 × 252 / 25

= 88 × 252 / 100

= 22176/100

= 221.76 unit²

Answer 2

Given :-

• Circumference = 52.8 cm

To find :-

• Area of the circle = ?

Solution :-

we know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{circumference=2\pi{r}}}}}$

Then,

⤇ 2πr = 52.8

$\rm\longrightarrow\:2\times\dfrac{22}{7}\times{r}=52.8$

$\rm\longrightarrow\:r=52.8\times\dfrac{7}{44}$

$\rm\longrightarrow\:r=\dfrac{369.6}{44}$

$\rm\longrightarrow\:r=8.4\:cm$

Now we have,

• radius = 8.4 cm

Area of circle = πr²

$\rm\:Area\:of\:circle=\dfrac{22}{7}\times{(8.4)}^{2}$

$\rm\:Area\:of\:circle=\dfrac{22}{7}\times{8.4}\times{8.4}$

Area of circle = 22 × 1.2 × 8.4

Area of circle = 221.76 cm²

Hence,area of the circle will be 221.76 cm².

More Information :-

Circumference and area of circle,

• circumference of the circle = 2πr
• Area of the circle = πr²
• Area of the semicircle = ½ πr²
• perimeter of the semicircle = (πr + 2r)

Related to sector or segment,

• Area of sector = θ/360° × πr²
• Angle of the sector = 360° × A/πr²
• perimeter of the sector = 2πrθ/360° + 2r