Question

Solve .
A military tent of height 8.25 m is the form of a right circular cylinder of base diameter 30m and height 5.5m surmounted by a right circular cone of same base radius . Find the lenght of the canvas use in making the tent , if the breadth of the cancas is 1.5m .

Answer 1

Height of the cone = 8.25 - 5.5= 2.75 m
Slant height of the cone(l)= Under root h^2 + r^2 = 15.25
surface area of cone= pie x r x l = 3.14 x 15 x 15.25= 718.3
surface area of cylinder = 2 x pie x r x h = 2 x 3.14 x 15 x 5.5= 518.1
area of canvas used = 718.3 + 518.1 =1236.4
length of canvas = 1236.4/1.5= 824.3 m 

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Answer 2

Given condition ⇒ 
Height of the Tent = 8.25 m.

For the Cylinder,
Diameter = 30 m.
∴ Radius (r) = 15 m.
Height(H) = 5.5 m.

For the cone,
Radius = 15 m. [∵ Radius of both the cylinder and the cone is same.]
Height of the cone(h) = 8.25 - 5.5
= 2.75 m.

∴ l = $\sqrt{ 2.75^{2} + 15^{2} }$
∴ l = √232.5625 
∴ l = 15.25 m

Now, Refers to the attachment.

Curved surface area of the cylinder = 2πrh
= 2 × 22/7 × 15 × 5.5
= 3630/7 m²

Curved surface area of the cone = πrl
= 22/7 × 15 × 15.25
= 5032.5/7 m².

∴ Total curved surface area of the tent = Curved surface area of the Cylinder + Curved surface area of the cone.
= 3630/7 + 5032.5/7
= 8662.5/7
= 1237.5 m².

Now, Area of the canvas which is used in making the tent is equal to the Total curved surface area of the tent.
∴ (length × Breadth) of the Canvas = 1237.5 m²
∴ Length = 1237.5/1.5
∴ Length of the Canvas = 825 m


Hence, the length of the Canvas is 825 m.


Hope it helps.