Question

A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)​

Answer 1

$\huge\tt \underline \red{Question}$

A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)

$\rm \underline \red{Given \: :}$

• Diameter of flower bed.
• Radius of path surrounded by flower bed.

$\rm \underline \red{To \: Find \ :}$

• Area of path.

$\huge\rm \underline \red{Solution╭☞}$

First, find area of flower bed↓

Radius $= \frac{66}{2} = 33m$

Area of flower bed $\red{ = \pi r {}^{2} }$

$= 3.14 \times 33 \times 33$

$= 3.14 \times 1089$

$= 3419.46 {m}^{2}$

Now, We'll find area of Path ↓

Radius of circle 2$\sf { \{Radius \: of \: inner \: circle + Radius \: of \: path} \}$

$= (33 + 4) = 37$

Area of circle 2$\red{= \pi r {}^{2} }$

$= 3.14 \times 37 \times 37$

$= 3.14 \times 1369$

$= 4298.66 {m}^{2}$

So, Now Area of path (Shaded region) = Area of Circle 2 - Area of flower bed

$\fbox{4298.66 - 3414.46}$

$\fbox{ = 879.2 m²}$

Hence, Area of path is 879.2m².

Hope It Helps You! ツ

Answer 2

GIVEN:-

• Flowers bed is surrounded by a path of 4 metres.
• Diameter of flower bed is 66 metres.

TO FIND:-

• Area of path?

SOLUTION:-

Area of flower bed:-

$\large \boxed { \red{\pi {r}^{2}}}$

$3.14 \times { (\frac{66}{2} )}^{2}$

$= 3.14 \times {33}^{2}$

$= 3.14 \times 1089$

${3419.46}^{2}$

Area of outer circle:-

$\large {\boxed {\red{\pi {r}^{2}}}}$

$3.14 {(radius \: of \: path) + (radius \: of \: flower \: bed)}^{2}$

$= 3.14 {\times (33 +4)}^{2}$

$= 3.14 \times {37}^{2}$

$3.14 \times 1369$

${4298.66}^{2}$

Area of path:-

${\red{Area \: of \: outer \: circle - area \: of \: flower \: bed}}$

${4298.66 - 3419.46}$

$\large \boxed{{879.2}^{2}}$

Hence, Area of path is ${879.2m}^{2}$