Question

The length of a semicircular tunnel is $2$ $km$ and diameter is $7$ $m$. Find the expenditure for digging the tunnel at the rate of Rs. $600$ per $m^3$. Find the expenditure for plastering inner side of the tunnel at the rate of Rs. $50$ per $m^2$. $(\pi =\frac{22}{7})$

Answer 1

Length of the semicircular tunnel $=2$ $km$.
$\therefore l=2000$ $m$
Diameter of the semicircular tunnel $=7$ $m$
$\therefore$ Radius of tunnel $=\frac{7}{2}$
$\therefore r=3.5$ $m$
Volume of semicircular tunnel $=\frac{1}{2}\times$ Volume of circular tunnel
$=\frac{1}{2}\times \pi r^{2}l$
$=\frac{1}{2}\times \frac{22}{7}\times 3.5\times 3.5\times 2000$
$=11\times 0.5\times 3.5\times 2000$
$=11\times 5\times 35\times 20$
$=38500m^3$
$\therefore$ Expenditure for digging (semicircular) the tunnel at the rate Rs. $600$ per $m^3$
$=38,500\times 600$
$=$ Rs. $2,31,00,000$
$\therefore$ Expenditure for plastering inner side of the tunnel at the rate of Rs. $50$ per $m^2$
$=22000\times 5$
$=$ Rs. $11,00,000$