Q. 94.1( 40 Votes )

# A military tent o

Answer :

The military tent is made as a combination of right circular cylinder and right circular cone on top.

Total Height of tent = h = 8.25 m

Base diameter of tent = 30 m

Base radius of tent = r = 30/2 m = 15 m

Height of right circular cylinder = 5.5 m

Curved surface area of right circular cylindrical part of tent = 2πrh

Height of conical part = total height of tent – height of cylindrical part

h_{cone} = 8.25 – 5.5 m = 2.75 m

Base radius of cone = 15 m

Let l be the slant height of cone

Then, l^{2} = h_{cone}^{2} + r^{2} = 2.75^{2} + 15^{2} m^{2}

l^{2} = 7.5625 + 225 m^{2} = 232.5625

l = 15.25

Curved surface area of conical part of the tent = πrl

Total surface area of the tent = Curved surface area of cylindrical part + curved surface area of conical part

Total surface area of tent = 2πrh + πrl

= πr (2h + l)

= 22/7 × 15 × (2 × 5.5 + 15.25) m^{2}

= 22/7 × 15 × (11 + 15.25) m^{2}

= 22/7 × 15 × 26.25 m^{2}

= 1237.5 m^{2}

Breadth of canvas used = 1.5 m

Length of canvas used = Total surface area of tent ÷ breadth of canvas used

Length of canvas used = 1237.5\1.5 m = 825 m

∴ Length of canvas used is 825 m.

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