Question

In a society, the management wants to put a circular fountain at the centre of the square park with diameter 14 m. The remaining area is to be covered with grass. If the cost of laying grass is Rs. 20/ $m^2$ and cost for constructing the fountain is 10/$m^2$. Find the length of the field if the total cost incurred is Rs. 6460. $(Use\pi =\frac{22}{7})$

• A. 20 m
• B. 25 m
• C. 32 m
• D. 30 m

Answer 1

The correct option is A

20 m

Diameter = 14m, so radius = 7m.

Let the length of the square be ‘a’.

Let the length of the square be ‘a’.

Total cost = cost of fountain + cost of grass

= (Area of fountain x cost for constructing the fountain) + (Area of square – Area of circle) x cost for grass)

$\Rightarrow$ 6460 = ($\pi \times 7^2$ $\times$ 10) + ($a^2-\pi \times 7^2)$ $\times$ 20

$\Rightarrow$ 6460 = (154 $\times$ 10) + (($a^2$ - 154) $\times$ 20)

$\Rightarrow$ 6460 = 1540 + ( $a^2$ -154) $\times$ 20

$\Rightarrow$ a = 20

Hence, side of square park is 20 m.