Question

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

• A. 20 m
• B. 40 m
• C. 30 m
• D. 21 m

Answer 1

The correct option is A

20 m

Diameter of a circular fountain= 14m, so radius = 7m.

Let the length of the square be $a$ m and radius of the fountain be $r$ m

Total cost = cost of constructing the fountain + cost of laying the grass

6460 = (area of fountain x cost per $m^2$) + (Area of square park -area of circular fountain) x (cost for grass per $m^2$)

$6460=\left(\pi \right(r{)}^2\times 10)+((a^2-\pi (r{)}^2)\times 20)$

$6460=\left(\pi \right(7{)}^2\times 10)+((a^2-\pi (7{)}^2)\times 20)$

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

$6460=1540+(a^2-154)\times 20$
$6460-1540=(a^2-154)\times 20$
$4920=(a^2-154)\times 20$
$246=(a^2-154)$
$246+154=a^2$
$400=a^2$

$a=20m$