A solid cylinder of radius \(r\) and height \(h\) is placed over another cylinder of same height and radius. The total surface area of the shape so formed is \(4\pi rh + 4\pi r^2\).
Step 1: Understand the situation.
We have two identical cylinders. Each has radius \(r\) (in metres) and height \(h\) (in metres). When one is placed on top of the other, we get a single tall cylinder of:
Height = \(h + h = 2h\) (in metres).
Radius = \(r\) (remains the same, in metres).
Step 2: Recall the formula for total surface area (TSA) of a cylinder:
\[ \text{TSA} = 2\pi r h + 2\pi r^2 \]
Here:
Step 3: Apply the formula to the new cylinder.
For height = \(2h\), radius = \(r\):
\[ \text{TSA} = 2\pi r(2h) + 2\pi r^2 \]
Simplify:
\[ \text{TSA} = 4\pi r h + 2\pi r^2 \]
Step 4: Compare with the given statement.
The question says TSA = \(4\pi rh + 4\pi r^2\).
But we found TSA = \(4\pi rh + 2\pi r^2\).
Final Answer: The given statement is incorrect. So the answer is False.