Question

8. The diameter of the flower bed is 56 cm. if this has to be surrounded by a path 7 cm wide, what is the area
of this path?

​

Answer 1

Answer :

The area of path = 2386 cm²

We are given :

• Diameter of a flower bed = 56 cm
• The flower bed is surrounded by a path of width = 7 cm

Need to find :

• Area of the path

Solution :

To find the area of path, firstly we will calculate the radius of the flower bed by using the following formula :

→ Radius = Diameter ÷ 2

Substituting the given values :

→ Radius = 56 ÷ 2

→ Radius = 28

Radius of the flower bed = 28 cm

Now, we can calculate the area of flower bed as we have the value of radius of the flower bed $.$

→ Area of flower bed = πr²

where,

• Take π = 22/7
• r denotes the radius

Substituting the given values :

→ Area of flower bed = 22/7 × (28)²

→ Area of flower bed = 22/7 × 28 × 28

→ Area of flower bed = 22 × 4 × 28

→ Area of flower bed = 2464

Therefore, the area of flower bed = 1464 cm²

Now, we will calculate the area of flower bed including the path. For calculating that we need the value of radius of the flower bed including the path. So, add the width of the path to the radius of the flower bed, the resultant value will be the radius of the flower bed including the path.

→ Radius of flower bed including the path = Radius of flower bed + Width of the path

→ Radius of flower bed including the path = 28 + 7

→ Radius of flower bed including the path = 35

Therefore, the radius of flower bed including the path = 35 cm

Now, we will calculate the area of flower bed including the path :

Using formula,

Area of flower bed including the path = πr²

Substituting the given values :

→ Area of flower bed + path = 22/7 × (35)²

→ Area of flower bed + path = 22/7 × 35 × 35

→ Area of flower bed + path = 22 × 5 × 35

→ Area of flower bed + path = 3850

Therefore, the area of flower bed including the path = 3850 cm²

Now, we can calculate the area of path, by subtracting the area of flower bed from area of flower bed including the path.

→ Area of path = Area of flower bed + path - Area of flower bed

→ Area of path = 3850 - 1464

→ Area of path = 2386

Therefore, the area of path = 2386 cm²