A closed cylinder tank of radius 7 m and height 3 m is made from a sheet of metal. How many sheets of metal are required?
VerifiedHint: The cylinder is a three-dimensional shape with two round shapes at either end and has two parallel lines connecting the round ends. These two round shapes are the base of the cylinder and their centers are joined by a line segment.
A cylinder is one of the most basic curved geometric shapes whose surface is formed by the point at a fixed distance from a given line segment.
A cylinder is a combination of a curved sheet with two round shapes from both sides, hence finding the amount of sheet to make the cylinder find the surface area of the rectangular sheet and the two rectangular plates.
Complete step-by-step answer:
A cylinder is one of the most basic curved geometric shapes whose surface is formed by the point at a fixed distance from a given line segment.
A cylinder is a combination of a curved sheet with two round shapes from both sides, hence finding the amount of sheet to make the cylinder find the surface area of the rectangular sheet and the two rectangular plates.
Height \[h = 3m\] and, Radius \[r = 7m\]
Given the closed cylinder tank is made of metal sheet, therefore
Area of metal sheet= area of closed Cylinder Tank = Total surface area of the cylinder
A cylinder is made of a rectangular sheet and two circular plates, hence
The total surface area of Cylinder= Area of the metal sheet + Area of the base
\[
TSA = 2\pi rh + 2\pi {r^2} \\
= \left( {2 \times \dfrac{{22}}{7} \times 7 \times 3} \right) + \left( {2 \times \dfrac{{22}}{7} \times 7 \times 7} \right) \\
= \left( {44 \times 3} \right) + \left( {44 \times 7} \right) \\
= 132 + 308 \\
= 440{\text{ }}{m^2} \\
\]
Hence the total metal sheet required for the cylinder is \[440{m^2}\].
Note: Students can also find the surface area of the cylinder by opening the cylinder vertically from its lateral surface, then they will get a rectangular shape and two circles hence they can find the area of figures separately.
