Question

A rectangular strip of $ 25cm\times 7cm $ is rotated about the longer side. Find the total surface area of solid thus generated.

Answer 1

Hint: First, firstly draw a rectangular strip with length 25cm and breadth 7 cm. Then, we know when we rotate a rectangle along a longer side, we get a cylinder of height same as rectangle length and radius of base same as rectangle breadth. Then, we know the formula of the total surface area A of the cylinder is given by $ A=2\pi r\left( h+r \right) $ . Then, by substituting the value of r as 7cm and value of h as 25 cm from the above figure to get the total surface area of the cylinder.

Complete step-by-step answer:
In this question, we are supposed to find the total surface area of solid generated by rotating the rectangular strip of dimensions $ 25cm\times 7cm $ .
So, firstly draw a rectangular strip with length 25cm and breadth 7 cm.

Then, we are said to rotate the above rectangle along the longer side which is 25cm to get a new solid shape.
Thus, we know when we rotate a rectangle along a longer side, we get a cylinder of height same as rectangle length and radius of base same as rectangle breadth.

Now, we are asked to find the total surface area of the solid which is cylinder obtained.
The, we know the formula of the total surface area A of the cylinder is given by:
 $ A=2\pi r\left( h+r \right) $
Now, by substituting the value of r as 7cm and value of h as 25 cm from the above figure to get the total surface area of the cylinder as:
 $ A=2\pi 7\left( 25+7 \right) $
Now, solve for the value of total surface area as:
 $ \begin{align}
  & A=14\pi \left( 32 \right) \\
 & \Rightarrow A=448\pi \\
 & \Rightarrow A=1406.72 \\
 & \Rightarrow A=1407c{{m}^{2}} \\
\end{align} $
So, the total surface area of the cylinder is $ 1407c{{m}^{2}} $ .
Hence, the solid obtained by rotating the rectangle total surface area is $ 1407c{{m}^{2}} $ .

Note: Now, to solve these types of questions we need to know some of the basic formulas of the figures to get the answer. Here, some of the basic formulas required as:
Total surface area of the cylinder is given by $ 2\pi r\left( h+r \right) $ .
Curved surface area of the cylinder is given by $ 2\pi rh $ .