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. - Mathematics

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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 2.8 cm and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (use `pi =22/7`)

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Solution

Height of conical upper part = 3.5 m, and radius = 2.8 m

(Slant height of cone)2 = 2.12+ 2.82 = 4.41 + 7.84

Slant height of cone = `sqrt(12.25)=3.5 m`

The canvas used for each tent = curved surface area of cylindrical base + curved surface area of conical upper part

= 2πrh+πrl

=πr(2h+ l)

`=22/7xx2.8(7+3.5)`

`=22/7xx2.8xx10.5`

= 92.4 m2

So, the canvas used for one tent is 92.4 m2 .

Thus, the canvas used for 1500 tents = (92.4 x 1500) m2 .

Canvas used to make the tents cos t Rs. 120 per sq. m

So canvas used to make 1500 tents will cos t Rs. 92.4 x 1500 x 120.

The amount shared by each school to set up the tents

= `(92.4xx1500xx120)/50="Rs." 332640`

The amount shared by each school to set up the tents is Rs.332640.

The value to help others in times of troubles is generated from the problem.

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2015-2016 (March) All India Set 1

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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 2.8 cm and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (use `pi =22/7`)


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