Five geometric blocks with their dimensions are given below. Calculate the length of the path as shown in the image below, between points A and B.
Show Hint
When finding the shortest path on solid surfaces:
\begin{itemize}
\item Unfold the faces mentally or on paper,
\item Replace slanted paths with diagonals of rectangles,
\item Add all contributing straight-line distances carefully.
\end{itemize}
Step 1: Observe that the red path consists of straight-line segments drawn over the faces of the blocks. Each segment corresponds to a horizontal or slanted distance across rectangular or cylindrical faces.
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Step 2: Add the horizontal distances along the base blocks:
\[
1 \text{ cm} + 2 \text{ cm} + 1 \text{ cm} + 1 \text{ cm} = 5 \text{ cm (approximately)}.
\]
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Step 3: Include the additional slanted portions formed due to height differences between adjacent blocks. These slanted paths are diagonals on rectangular faces and contribute extra length beyond the horizontal projection.
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Step 4: Accounting for the diagonal contributions and curved transition over the cylindrical block, the total additional length is approximately:
\[
1 \text{ cm to } 1.5 \text{ cm}.
\]
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Step 5: Hence, the total path length from A to B is:
\[
\text{Path length} \approx 5 + (1 \text{ to } 1.5) = 6 \text{ to } 6.5 \text{ cm}.
\]
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