Question

Find the area of the sheet required to make a cylindrical container which is opened at one side and whose diameter is \[28cm\] and height is \[20cm\]. Find the approximate area of the sheet required to make the lid of height \[2cm\] for this container.

Answer 1

Hint: Firstly calculate the surface area of the cylinder whose one end is open. And then calculate the surface area of the sheet for the lid of height \[{\text{2cm}}\]and adding both of them our required answer will be obtained.

Complete step-by-step answer:
As per the given, the radius and height of the cylinder given is \[{\text{14cm}}\] and \[{\text{20cm}}\].

Now, the surface area of cylinder with one side open is \[{{A = 2\pi rh + \pi }}{{\text{r}}^{\text{2}}}\]
So,
\[{{A = 2\pi rh + \pi }}{{\text{r}}^{\text{2}}}\]
On substituting the value of r and h, we get,
\[
  {{ = 2\pi (14)(20) + \pi (14)(14)}} \\
  {{ = (560 + 196)\pi }} \\
  {{ = 2376}}{{\text{cm}}^{\text{2}}} \\
 \]
On simplifying and multiplying the term with \[{{ \pi = 3}}{\text{.14,}}\]we get
\[{{ = 2373}}{\text{.84c}}{{\text{m}}^{\text{2}}}\]
And now, calculate just the surface cylindrical area of the lid whose height is 2cm is,
\[{{A = 2\pi rh + \pi }}{{\text{r}}^{\text{2}}}\]
On substituting the value of r and \[{\text{h'}}\],we get
\[
  {{ = 2\pi (14)(2) + \pi (14)(14)}} \\
  {{ = (56+ 196)\pi }} \\
  {{ = 792}}{{\text{cm}}^{\text{2}}} \\
 \]

Note: A cylinder is one of the most basic curved geometric shapes, with the surface formed by the points at a fixed distance from a given line segment, known as the axis of the cylinder. The shape can be thought of as a circular prism. Both the surface and the solid shape created inside can be called a cylinder.
The total surface area (TSA) includes the area of the circular top and base, as well as the curved surface area (CSA).