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

Solution

Height of the cylindrical part, H = 4 m

Height of the conical part, h = 2.8 m
Radius of the base, r = 2.1 m

So comma space straight l equals space square root of straight r squared space plus space straight h squared end root rightwards double arrow space straight l space equals space square root of left parenthesis 2.1 right parenthesis squared space plus left parenthesis 2.8 right parenthesis squared end root rightwards double arrow space straight l space equals space square root of 12.25 end root rightwards double arrow space 1 space equals space 3.5 space straight m surface space area space of space canvas space to space be space used space space equals space CSA space of space conical space part space plus space CSA space of space cylindrical space part space equals space πrl space plus space 2 πrH space equals space πr space left parenthesis straight l plus 2 straight H right parenthesis space equals space 22 over 7 space straight x space 2.1 space straight x space left parenthesis 3.5 space plus 8 space right parenthesis equals space 75. space 9 space straight m squared

Cost of the canvas = Rs 100/ m²
So, total cost of the canvas to be used = 75.9 x 100 = Rs 7,590

therefore,
Amount that the association will have to pay for each tent
=50% of Rs 7590
= Rs (50/100) x 7590
= Rs 3,795
Therefore, Amount that the associations will have for 100 tent = Rs 3795 x 100
= Rs 379500
Hence, the amount that the associations will have to pay for 100 tents is Rs 3,79,500
The associations are showing humanity and their helpful nature.

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