# 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 - Mathematics

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 the amount, the associations will have to pay. What values are shown by these associations? [Use π=22/7]

#### Solution

Diameter of the tent = 4.2 m
Radius of the tent, r = 2.1 m
Height of the cylindrical part of tent, hcylinder = 4 m
Height of the conical part, hcone = 2.8 m
Slant height of the conical part, l

=sqrt(h_(

=sqrt((2.8)^2+(2.1)^2)

=sqrt(12.5)=3.5m

Curved surface area of the cylinder = 2𝜋r hcylinder
= 2 ×(22/7)× 2.1 × 4
= 22 × 0.3 × 8 = 52.8 m2
Curved surface area of the conical tent = 𝜋rl =(22/7)× 2.1 × 3.5 = 23.1 m2
Total area of cloth required for building one tent
= Curved surface area of the cylinder + Curved surface area of the conical tent
= 52.8 + 23.1
= 75.9 m2
Cost of building one tent = 75.9 × 100 = Rs. 7590
Total cost of 100 tents = 7590 × 100 = Rs. 7,59,000

Cost to be borne by the associations =759000/2= Rs. 3,79,500
It shows the helping nature, unity and cooperativeness of the associations.

Concept: Surface Area of a Combination of Solids
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