Question

A circular grassy plot of land, $42m$ in diameter, has a path $3.5m$ wide running round it on the outside. Find the cost of gravel ling the path at Rs. $4$ per square metre.

• A. Rs. $2002$
• B. Rs. $2003$
• C. Rs. $2004$
• D. Rs. $2000$

Answer 1

The correct option is A Rs. $2002$

We have, Radius of the plot $=21m$
Radius of plot including the path $=21+3.5=24.5m$
Area of the path $=\pi \left({24.5}^2\right)-\pi \left({21}^2\right)$
$=\pi ({24.5}^2-{21}^2)$
$=\pi (24.5-21)(24.5+21)$
$=\frac{22}{7}\times 3.5\times 45.5$
$=500.5m^2$
Total cost of gravelling the path $=500.5\times 4$
$=$ Rs. $2002$