Question

The area of circular playground is 22176 sq.m.Find the cost of fencing the ground at the rate of Rs.50 per meter

Answer 1

given area= 22176= π*r*r
therefore r=
$\sqrt{22176 \div \pi}$
= 84 m
the perimeter = 2πr
therefore perimeter = 2π *84= 527.5 m
therefore cost of fencing= 527.5* 50= 26375 ₹

Answer 2

$\large\underline\pink{Given:-}$

• The area of a circular playground is 22176 m²
• The rate of fencing is Rs. 50 per m.

$\large\underline\pink{To find:-}$

• Fine the cost of fencing ....?

$\large\underline\pink{Solutions:-}$

• Let radius of playground be r cm.

Area of circle = πr²

$\: \: \: \: \: \leadsto \: \: \pi \: {r}^{2} \: \: = \: \: {22176}$

$\: \: \: \: \: \leadsto \: \: \frac{22}{7} \: \times \: {r}^{2} \: \: = \: \: {22176}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: \frac{{\cancel{22176}} \: \times \: {7}}{\cancel{22}}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: {1008} \: \times \: {7}$

$\: \: \: \: \: \leadsto \: \: {r}^{2} \: \: = \: \: {7056}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: \sqrt{7056}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {84} \: m$

Circumference = 2πr

$\: \: \: \: \: \leadsto \: \: {2} \pi \: r$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{\cancel{7}} \: \times \: \cancel{84} \: m$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {12} \: m$

$\: \: \: \: \: \leadsto \: \: {528} \: m$

Now, the cost of fencing

⟹ 50 × 528

⟹ 26400

Hence, The the cost of fencing is 26400.

$\large\underline\pink{More \: Information:-}$

1. Circumference of a circle = 2πr
2. Area of a circle = πr²

• r = radius
• d = diameter
• π = 22/7 and 3.14