Question

A lawn is in the shape of a semi-circle of diameter 35 dm. The lawn is surrounded by a flower bed of width 3.5 dm all round. Find the area of the flower bed in dm².

Answer 1

Given: A lawn is a semicircle with diameter 35 dm, surrounded all round by a flower bed of width 3.5 dm.

Step-wise calculation:

1. Inner semicircle:

Diameter = 35 dm

⇒ Tadius r = `35/2`

= 17.5 dm

Area (inner semicircle)

= `1/2 xx π xx r^2` 

= `1/2 xx π xx 17.5^2` 

= `1/2 xx π xx 306.25` 

= 153.125π

2. Outer semicircle (including flower bed):

Outer radius

R = r + 3.5 

= 17.5 + 3.5 

= 21.0 dm

Area (outer semicircle) 

= `1/2 xx π xx R^2`

= `1/2 xx π xx 21^2`

= `1/2 xx π xx 441`

= 220.5π

3. Area of flower bed

= Area (outer semicircle) – Area (inner semicircle)

= 220.5π – 153.125π

= 67.375π

= `539/8`π dm²

4. Numerical approximation (Take π = 3.14159265):

Area = 67.375 × 3.14159265

= 211.665 dm²   ...(Approximately)

The area of the flower bed is `539/8`π dm², which is approximately 211.665 dm².