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:

Diameter of the circular flower bed=66m

∴ Radius of circular flower bed(r)=

2

66

=33m

∴ Radius of circular flower bed with 4 m wide path(R)=33+4=37m

According to the question,

Area of path=Area of bigger circle−Area of smaller circle

=πR

2

−πr

2

=π(R

2

−r

2

)

=π[(37)

2

−(33)

2

]

=3.14[(37+33)(37−33)] [∵a

2

−b

2

=(a+b)(a−b)]

=3.14×70×4

=879.20m

2

.

Therefore, the area of the path is 879.20m

2

.

Answer 2

$\Large\sf\underline{Answer}$

Diameter of the circle = 66m

∴ Radius of the circle = $\Large\frac{66}{2}$ = 33m

Now, Area of the inner circle = $\pi$² = 33 × 33 × $\pi$ =

1089 × 3.14

∴ The area of the inner circle is $\rm\underline{3,419.46m²}$

Now, area of the circle with the path is =

Radius of the circle 33 + 4 = 37

Now, Area = 37 × 37 × $\pi$ =

1369 × 3.14

∴ Area of the circle with the path is $\rm\underline{4,298.66m²}$

Now we want to find the Area of the path.

Area of path = Area of circle with path - Area of circle without path.

Area of path = 4,298.66 - 3,419.46

∴Area of the path is $\large\rm\underline\orange{879.20m²}$