Question

Due to heavy floods in a state, thousands were rendered homeless. $50$ schools collectively offered to the state government to provide place and the canvas for $1500$ tents to be fixed by the governments and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius $2.8m$ and height $3.5m$, with conical upper part of same base radius but of height $2.1m$. If the canvas used to make the tents costs $Rs.120persq.m$ , find the amount shared by each school to set up the tents. Enter the answer in the nearest integer. $\left(\text{Use}\pi =\frac{22}{7}\right)$

Answer 1

Total area of each Tent (Cylinder) $=2\pi rh$

$=2\times \frac{22}{7}\times 2.8\times 3.5$

$=61.6$ $m^2$

Area of conical upper part (cone) $=$ $\pi rl$

$=\frac{22}{7}\times 2.8\times \sqrt{{2.1}^2+{2.8}^2}$

$=30.8$ $m^2$

Area of $1500$ tents $=$ Area of cylinder $+$ Area of cone

$=61.6+30.8$

$=92.4$ $m^2$

Cost of making Tent $=$ Rs. $120$ per $m^2$

Total money cost for canvas $=120\times 90.4$

$=$ Rs. $11088$

Amount shared by each school $=\frac{\text{Total amount}}{\text{Number of school}}$

$=\frac{11088}{50}$

$=$ Rs. $221.76$

Therefore, the amount shared by each school to set up the tents $=$ Rs. $221.76=Rs.222$ (approx)