#### Question

A tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per m^{2} ?

#### Solution

Given that height of a tent = 77dm

Height of cone = 44dm

Height of a tent without cone = 77 - 44 = 33dm

= 3.3m

Given diameter of cylinder (d) = 36m

Radius (r) = `36/2`= 18m

Let ‘l’ be slant height of cone

`l^2=r^2+h^2`

`l^2=18^2+3.3^2`

l^{2} = 324 + 10.89

l^{2} = 334.89

l = 18.3

Slant height of cone l = 18.3

Curved surface area of cylinder (S_{1}) = 2πrh

= 2 x π x18 x 4.4m^{2} ............(1)

Curved surface area of cone (S_{2}) = πrl

= π18 x 18.3m^{2 } .............(2)

Total curved surface of tent = S_{1} + S_{2}

_{T.C.S.A = }S_{1} + S_{2}

= 1532.46m^{2}

Given cost canvas per m^{2} = RS 3.50

Total cost of canvas per 1532.46 X 3.50

= 1532.46 X 3.50

= 5363.61

∴ Total cost of canvas = Rs 5363.61