Question

A flower bed which is circular in shape is surrounded by a path 5m wide. The diameter of a flower bed is 70m. What is the area of this path?

Answer 1

Diameter of flower bed = 70 m

Radius of flower bed = \frac{65}{2}=32.5 m

2

65

=32.5m

Width of path = 5 m

Outer radius = 32.5+5=37.5 m

Area of path = Outer path - Inner path

Area of path = \pi R^2-\pi r^2 = \frac{22}{7} \times 37.5^2-\frac{22}{7} \times 32.5^2=1100 m^2πR

2

−πr

2

=

7

22

×37.5

2

−

7

22

×32.5

2

=1100m

2

Hence The area of path is 1100 sq.m.

Answer 2

Answer:

Let r be the radius of the circular flower bed, and R be the radius of the outer circle consisting of the circular flower bed and the path surrounding it.

$then \: r \: = \frac{720}{2} \: m = 35 \: m \: and \\ \: R = (r \: + width \: of \: the \: path) \: =( 35 + 5)m = 40m$

Area of the path = Area of the outer circle - Area of the inner circular flower bed

= π R² - π r² = π(R²- r²)

= [3.14(40² - 35²)]m²

= [3.14(40 + 35)(40- 35)] m²

= (3.14 × 75 × 5)m² = 1177.5m²

✅ Hence the area of the path is 1177.5m².

Hope it helps you ⛄