Question

the Length of canvas 1.2m wide required to build a conical tent of height 14m and the floor area 346.5sqm ,is :
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Answer 1

solution:

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let l be the required length of canvas. here we have given that width of canvas = 1.2 m

Find the area of canvas :

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Area of canvas = length × width

= l × 1.2= 1.2l m^2

givne that floor area of conical tent

= 346.5 m^2

since , we know that floor of cone is circular.so then,

area of circle = floor area of conical tent

πr^2 = 346.5

solve for 'r' :

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r^2 = 346.5 × 7/ 22 = 2425.5 ÷ 22

r^2 = 110.25 => r = √110.25 = 10.5 m

thus , radius of cone = 10.5 m

since, we have given height of tent = 14m

Find the slant height:

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slant height (l) = √ [ (r)^2 + (h)^2 ]

l = √ [ ( 10.5)^2 + ( 14 )^2 ]

l = √(110.25 + 196 ) = √306.25

l = 17.5m, slant height = 17.5 m

Find the CSA of tent :

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curved surface area of conical tent = πrl

= 22/ 7 ×( 10.5) × 17.5

= 4042.5 ÷ 7 = 577.5 m^2

Find the length of Canvas:

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area of canvas =CSA of conical tent

1.2l = 577.5 => l = 577.5 ÷ 1.2

l = 481.25 m

therefore, the required length of canvas = 481.25 m

Answer : length = 481.25 m