A closed aquarium of dimensions 30 cm × 25 cm × 20 cm is made up entirely of glass plates held together with tapes. The total length of tape required to hold the plates together (ignore the overlapping tapes) is (Hotel Management, 2009)
Aptitude
Volume and Surface Area
Difficulty: Easy
Choose an option
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A75 cm
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B120 cm
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C150 cm
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D300 cm
Answer
Correct Answer: 300 cm
Explanation
### Concept & Total Length of Edges
The tape is used along the joints of the glass plates. Since it's a cuboidal aquarium, the joints correspond exactly to the edges of the cuboid.
$$\text{Total Edge Length} = 4(l + b + h)$$
### Step-by-Step Solution
* **Given:** Length ($l$) = $30\text{ cm}$, Breadth ($b$) = $25\text{ cm}$, Height ($h$) = $20\text{ cm}$.
* A cuboid has 12 edges in total: 4 lengths, 4 breadths, and 4 heights.
* **Step 1: Sum the dimensions**
Sum = $l + b + h = 30 + 25 + 20 = 75\text{ cm}$.
* **Step 2: Multiply by 4**
Total Tape Length = $4 \times 75\text{ cm} = 300\text{ cm}$.
### Exam Strategy & Shortcut
Recognize that "length of tape" means "perimeter of all faces combined but counted without overlap", which is just the sum of all edges. Add the three given numbers ($30+25+20 = 75$) and multiply by $4$.
### Common Pitfall
Many students calculate the surface area or volume by mistake, or they only sum $l + b + h$ once (Option A) or multiply by 2 (Option C) instead of 4.
### Final Answer
Therefore, the correct answer is **300 cm**.