Question

Sagar is a farmer. He owns many fields and farms. He works hard to earn his livelihood. In one of his fields he made a circular flower bed of radius 7m. He bought fertilizers for this flower bed. 100g fertilizers is needed for 1square metre area.
i) Find the area of the flower bed.
ii) Find the length of the boundary of the flower bed.
iii) How much fertilizers should Sagar purchase?

Answer 1

Answer:

1. The area of the flower bed = 154 m²
2. The length of the boundary of the flower bed = 44 m
3. Sagar should purchase 15.4 kg of fertilizers.

Step-by-step explanation:

Given that:

• Radius of a circular flower bed = 7 m
• Fertilizers is needed for 1 square metre area = 100 g

To Find:

1. Find the area of the flower bed.
2. Find the length of the boundary of the flower bed.
3. How much fertilizers should Sagar purchase?

Formula used:

• Area of a circle = π × (radius)²
• Circumference of a circle = 2 × π × radius

Finding the area of the flower bed:

• Area of flower bed = π × (7 m)²
• Area of flower bed = (22 × 7 m × 7 m)/7
• Area of flower bed = 154 m²

Finding the length of the boundary of the flower bed:

• Length of boundary = 2 × π × 7 m
• Length of boundary = (2 × 22 × 7 m)/7
• Length of boundary = 44 m

Finding the amount of fertilizers needed:

We have,

• Total area = 154 m²
• Fertilizers needed = 100 g/m²

• 1 m² area needed 100 g fertilizers.
• 154 m² area needed (100 × 154) g fertilizers.
• 154 m² area needed 15400 g fertilizers.

Converting amount of fertilizers in kg:

• 1000 g = 1 kg
• 1 g = 1/1000 kg
• 15400 g = 15400/1000 = 15.4 kg

Answer 2

Given

• Radius of circular flower bed (circle) = 7 m
• Amount of fertilizers needed for 1 m² - 100 g

To find

1. Area of the flower bed.
2. The length of the boundary of the flower bed.
3. How much fertilizers should Sagar purchase?

Solution

The flower bed is in the shape of circle, and we have the radius, so let's find the area of circle.

• Area of circle =  π(r)²
• Area of circle = 22/7 × 7 × 7
• Area of circle = 154

Hence, the area of circle is 154 m²

Now, we shall find the length of the boundary, boundary is nothing but the perimeter, and for circle it's called the circumference. Let's find it out.

• Perimeter of circle = 2πr
• Perimeter of circle = 2 × 22/7 × 7
• Perimeter of circle = 44

Hence, the circumference of circle is 44 m

Now, we have the area and let's find fertilizers.

• 1 m² - 100 g
• 154 m² - ?
• 154 m² = 100 × 154
• 154 m² = 15400

Hence, the amount of fertilizers required are 15400 g or 15.4 Kg