Question

A path of 4 m width runs round a circular grassy plot whose circumference a $163\frac{3}{7}$ m Find
(i) the area of the path
(ii) the cost of gravelling the path at the rate of $Rs.1.50$ per square meter
(iii) the cost of turfing the plot at the rate of 45 paise per $m^2$ .

Answer 1

Circumference of plot$=163\frac{3}{7}m$

$=\frac{1144}{7}m$

$\Rightarrow 2\pi r=\frac{1144}{7}$

$\Rightarrow r=\frac{1144\times 7}{7\times 44}$

$\Rightarrow r=26m$

i) Area of path$=\pi (R^2-r^2)$

$=\frac{22}{7}({(26+4)}^2-{\left(26\right)}^2)$

$=\frac{22}{7}\times 224$

$=704m^2$

ii) Cost of graveling

$=$ $(704\times 1.50)$

$=$ $Rs.1056$

iii) Area of plot$=\pi r^2$

$=\frac{22}{7}\times 26\times 26$

$=2124.57m^2$

$\therefore$ Cost of turfing at the rate of 45 paise per $m^2$

m2

$=Rs.(2124.57\times 0.45)$

$=Rs.956.06$