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Question
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.
Solution
Given diameter of cylinder = 24m
Radius`(r)=24/2=12m`
Given height of cylindrical part(h1) = 11m
∴ Height of cone part(h2) = 5m
Vertex of cone above ground = 11 + 5 = 16m
Curved surface area of cone(S1)= πrl
`=22/7xx12xxl`
Let l be slant height of cone
⇒ `l=sqrt(r^2+h_2^2)`
⇒ `l=sqrt(12^2+5^2`
l = 13m
∴ Curved surface area of cone `(5)=22/7xx12xx13m^2` ...........(1)
Curved surface area of cylinder(S2) = 2πrh
S2 = 2π(12)(11)m2 ..........(2)
To find area of canvas required for tent
S = S1 + S2 = (1) + (2)
`S=22/7xx12xx13+2pi(12)(11)`
S = 490 + 829.38
S = 1320m2
∴Total canvas required for tent(S) = 1320m2
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