Question

6.A circular garden has a circum-
ference of 440m. There is a 7 m
wide border inside the garden
along its periphery. The area of
the border is : (in m)​

Answer 1

☆Given :

• Circumference = 440 m

• length between both gardens = 7 m

☆Solution :

$\large \boxed{ \boxed{ \red{circumfrence =2\pi \: r}}}$

$\implies$ 440m = 2 × 22/7 × r

$\implies \: 440m = \large\frac{44}{7} \small\times r$

$\bigstar$ On transposing the terms:

$\: \: \: \: \: \: \: \rightarrow \: \: \: \: \large \frac{440 \times 7}{44} \small = radius$

$\implies \: radius \: = 10 \times 7$

$\bigstar$ radius = 70m

• Since, distance between both gardens = 7m

$\therefore$ radius of inner circle or garden:

= 70 - 7

= 63 m

$\huge{ \boxed{ \boxed{{ \red{now}}}}}$

Area of outer circle :

$\: \: \: \: \: \: \: \rightarrow \pi r²$

$\implies \: area = \large\frac{22}{7} \small \times {70}^{2}$

$\implies \: \large\frac{22}{7} \small\times 70 \times 70$

$\implies$ 22 × 10 × 70

$\implies$ 22 × 700

$\therefore$ area = 15,400 m²

area of inner circle :

$\: \: \: \: \: \: \: \rightarrow \pi r²$

$\implies \: area \: = \large \frac{22}{7} \small\times {63}^{2}$

$\implies \: \large\frac{22}{7} \small \times 63 \times 63$

$\implies$ 22 × 9 × 63

$\implies$ 198 × 63

$\therefore$ area = 12,474 m²

$\: \: \: \: \: \: \: \: \bigstar$ area of outer circle = 15,400 m²

$\: \: \: \: \: \: \: \: \bigstar$ area of inner circle = 12,474 m²

☆ Area of path :

= 15,400 m² - 12,474 m²

$\therefore \large \boxed{\purple{area \: of \: path \: = \: {2926m}^2} }$