Question

4. A park is in the form of a rectangle 100 m x 80 m.
At the centre of the park there is a circular
lawn. The area of the park excluding the lawn
is 4150 m? Find the radius of the circular
lawn (Fig. 13.81)
80 m
100 m​

Answer 1

Answer:

Question:-

• A park is in the form of a rectangle 100 m x 80 m. At the centre of the park there is a circular lawn. The area of the park excluding the lawn is 4150 sq. m. Find the radius of the circular lawn?

Answer

Given :-

• Length of Rectangular Park = 100 m
• Breadth of Rectangular Park = 80 m
• At the centre of the park there is a circular lawn.
• The area of the park excluding the lawn is 4150 sq. m.

To find:-

• Radius of circular lawn.

Formula used :-

$\underline{\boxed{\sf \: Area \: of \: Rectangle = length \times breadth }}$

$\underline{\boxed{\sf Area \ of \ circle = \pi \: {r}^{2} }}$

Solution :-

Length of Rectangular Park = 100 m

Breadth of Rectangular Park = 80 m

Area of Rectangular Park = 100 × 80 = 8000 m²

Let the radius of circular lawn = 'r' m

Area of circular lawn =  πr²

According to statement

The area of the park excluding the lawn is 4150 m²

Area of Rectangular Park - Area of circular lawn = 4150 m²

$\bf\implies \:8000 - \pi \: {r}^{2} = 4150$

$\bf\implies \:\pi \: {r}^{2} = 3850$

$\bf\implies \:\dfrac{22}{7} \times {r}^{2} = 3850$

$\bf\implies \: {r}^{2} = \dfrac{3850 \times 7}{22}$

$\bf\implies \: {r}^{2} = 175 \times 7$

$\bf\implies \:r = 5 \times 7 = 35 \: m$

__________________________________________