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A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m2, is:
80π
160π
200π
40π
80π
The required surface area for a cylinder (excluding ends) is simply the circumference (π∗d)times the length (h). So, π∗2∗40=80π.
Diameter of the cylinder d = 2 m, Length of the cylinder h = 40 m
A=π×d×h
The required surface area for a cylinder (excluding ends) is simply the circumference (π∗d)times the length (h). So, π∗2∗40=80π.
Students often use the full surface area formula 2πrh+2πr2 (including circular ends), but a tunnel is typically just the hollow cylindrical pipe/tube.
Identify Given Parameters
The tunnel is a cylinder with diameter d=2 m and length (height) h=40 m.
d=2,h=40
Select Formula
Since the tunnel is an open-ended cylinder, we only need the lateral surface area of the cylinder.
A=π×d×h
Calculate Area
Substitute the values into the formula: A=π×2×40.
A=80π
A is correct because the lateral surface area of a cylindrical tunnel is calculated by multiplying the circumference (π∗d)by the length, which equals 80πm².
This concept frequently appears in competitive exams related to calculating material requirements for pipes, wires, or road construction where only the side surface matters, not the area of the circular ends.
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