Question:medium

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 \(\text{cm}^2\).
Reason (R) : The surface area of a cuboid of dimensions \(l \times b \times h\) is \((lb + bh + hl)\).

Show Hint

An alternative way to calculate the surface area of the joined cubes:
Two separate cubes have \(6 + 6 = 12\) faces in total.
When joined together, 2 faces (one from each cube) overlap and are hidden inside.
So, the surface area is the area of the remaining 10 exposed faces:
\[ \text{Surface Area} = 10 \times s^2 = 10 \times 4^2 = 10 \times 16 = 160\ \text{cm}^2 \]
This structural logic is very quick and visual!
Updated On: Jul 7, 2026
  • Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation of Assertion (A).
  • Assertion (A) is true, but Reason (R) is false.
  • Assertion (A) is false, but Reason (R) is true.
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Build the cuboid by adding up its six faces one at a time, instead of using the total surface area formula.
Joining two cubes of side 4 cm end to end gives a cuboid of length $l = 8$ cm, breadth $b = 4$ cm, and height $h = 4$ cm. A cuboid has 3 pairs of identical opposite faces:
Top and bottom faces: each measures $l \times b = 8 \times 4 = 32$ cm$^2$, giving $2 \times 32 = 64$ cm$^2$.
Front and back faces: each measures $l \times h = 8 \times 4 = 32$ cm$^2$, giving $2 \times 32 = 64$ cm$^2$.
Left and right faces: each measures $b \times h = 4 \times 4 = 16$ cm$^2$, giving $2 \times 16 = 32$ cm$^2$.

Step 2: Add all six faces to get the total surface area.
\[ \text{Total Surface Area} = 64 + 64 + 32 = 160 \text{ cm}^2 \]
This matches the value given in Assertion (A), so Assertion (A) is true.

Step 3: Test Reason (R) by plugging its own numbers in and comparing to the real answer.
Reason (R) claims the surface area equals $lb + bh + hl$. Plug in the same dimensions:
\[ lb + bh + hl = (8)(4) + (4)(4) + (4)(8) = 32 + 16 + 32 = 80 \text{ cm}^2 \]
This gives 80 cm$^2$, but the actual surface area worked out in Step 2 is 160 cm$^2$. Since $80 \neq 160$, the formula in Reason (R) does not give the correct surface area value, so Reason (R) is false (it is missing the factor of 2 that turns it into the correct total).

Step 4: Final Answer.
Assertion (A) is true, but Reason (R) is false, so option (C) is correct. \[ \boxed{\text{A is true, R is false}} \]
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