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?​

Answer 1

Answer:

880m²

Explanation:

Given that :—

• r = 66m ÷ 2 = 33m
• R = (33m + 4m) ÷ 2 = 37m

To be found :—

• Area of the path ( ring-shaped )

Placing all the given information in the formula to find out the area of a ring , we get :—

A = π(R² - r²) , where ,

• A is the area of the ring ( area of the path )
• R² is the outer radius ( radius of the flower bed to the path )
• r² is the inner radius ( radius of the flower bed )

Solution :—

A = 22/7(37m × 3m - 33m × 33m)

= 22/7(1369m² - 1089m²)

= 22/7 × 280m²

= 880m²

Answer 2

Given:

• A circular flower bed is surrounded by a path 4 m wide.
• The diameter of the flower bed is 66 m.

To Find:

• What is the area of this path?

Solution:

Concept: Here, It is said that the diameter of a circle is 66m and it is surrounded by a path of length 4m and we have to find the area of the path

We know that,

$\: \: \: \: \: \star \: \tt {\pink{ \boxed{ \tt{area \: of \: a \: circle = \pi {r}^{2} }}}}$

Now, let's find the area of the inner circle,

• Here,

➪ Diameter = 66m so,

➪  Radius = 66/2 = 33m

Substituting the values we get,

$\longrightarrow \tt \: area = \pi {r}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: area = 3.14 \times 33 \times 33 \\ \\ \\ \longrightarrow \tt \: area = 3419.46 {m}^{2} \: \: \: \: \: \: \: \: \:$

• Therefore area of the inner circle is 3419.46m²

Now, let's find the area of the outer circle,

• Here,

➪ Radius = 33m + 4m

➪ Radius = 37m

Substituting the values we get,

$\longrightarrow \tt \: area = \pi {r}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: area = 3.14 \times 37 \times 37 \\ \\ \\ \longrightarrow \tt \: area = 4298.66 {m}^{2} \: \: \: \: \: \: \: \: \:$

• Hence, the area of the other circle is 4298.66m²

Now, let's find the area of the path,

We know,

$\: \: \: \: \: \star \: \tt {\pink{ \boxed{ \tt{area \: of \: a \: path = circle_{2} - circle_{1}}}}}$

Applying the concept,

$\longrightarrow \tt \: area \: of \: path = circle_{2} - circle_{1} \\ \\ \\ \longrightarrow \tt \: area \: of \: path = 4298.66 - 3419.46 \\ \\ \\ \longrightarrow \tt \: area \: of \: path = { \boxed{ \tt{879.2 {m}^{2} }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

• The area of the path is 879.2m²