Seven identical cubes, each of side 5 cm, are joined end-to-end to form a cuboid. Find the total surface area (in cm^2) of the resulting cuboid.

Difficulty: Easy

Correct Answer: 750 sq cm

Explanation:


Introduction / Context:
Joining seven cubes of side 5 cm end-to-end yields a cuboid whose dimensions can be inferred. Then use the total surface area formula for a cuboid: TSA = 2(lw + lh + wh).


Given Data / Assumptions:

  • Each cube side = 5 cm.
  • Seven cubes in a line ⇒ length = 7 * 5 = 35 cm; width = 5 cm; height = 5 cm.


Concept / Approach:
Compute TSA with l = 35, w = 5, h = 5.


Step-by-Step Solution:

TSA = 2(lw + lh + wh)= 2(35*5 + 35*5 + 5*5) = 2(175 + 175 + 25) = 2 * 375 = 750 cm^2


Verification / Alternative check:
Count exposed faces mentally: long faces (2), side faces (2), end faces (2) match TSA formula result.


Why Other Options Are Wrong:
They stem from forgetting one pair of faces or miscomputing one product.


Common Pitfalls:
Treating it as seven separate cubes and double-counting internal faces; arithmetic slips in multiplication.


Final Answer:
750 sq cm

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