Question

Due to sudden floods,some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m and the canvas to be used costs Rs 100 per sq m. Find amount the associations will have to pay. What values are shown by these associations?

Answer 1

Diameter of the tent (d)=4.2 m

$\therefore$ Radius of the tent (r)=2.1 m $[\therefore r=\frac{d}{2}]$

Height of the cylindrical part of tent (h)=4 m

Height of conical part (H)=2.8 m

Slant height of conical part(l)=$\sqrt{H^2+r^2}$

$l=\sqrt{(2.8{)}^2+(2.1{)}^2}$

$l=\sqrt{7.84+4.41}$

$l=\sqrt{12.25}$

$l=3.5m$

Curved surface area of the cylinder=$2\pi rh$

$=2\times \frac{22}{7}\times 2.1\times 4[\because \pi =\frac{22}{7}]$

$=2\times 22\times 0.3\times 4$

$=52.8m^2$

Curved surface area of conical tent=$\pi rl$

$=\frac{22}{7}\times 2.1\times 3.5$

$=22\times 0.3\times 3.5$

$=23.1m^2$

Total area of cloth required for building one tent=C.S.A of cylinder+C.S.A of conical tent

$=(52.8+23.1)m^2$

$=75.9m^2$

Cost of building one tent=$75.9\times 100$ = Rs 7590

Total cost of 100 tents=Rs$(7590\times 100)$ = Rs 7,59,000

Cost to be borne by the associations (50% of the cost)

$=\frac{75900\times 50}{100}$ = Rs 379500

Hence,the association are helping the flood victins and showing concern for humanity.