Question

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 \( (lb + bh + hl) \).

Hint:

Watch out for partial formulas in the Reason section of Assertion-Reason questions.

Answer 1

Assertion (A):
The surface area of the cuboid formed by joining two cubes of side 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 \[ (lb + bh + hl) \]

Step 1: Check Assertion (A)
When two cubes of side 4 cm each are joined end-to-end, the resulting cuboid has:
\[ l = 8\ \text{cm},\quad b = 4\ \text{cm},\quad h = 4\ \text{cm} \]
Surface area of cuboid:
\[ 2(lb + bh + hl) \]
Substitute values:
\[ 2(8 \times 4 + 4 \times 4 + 4 \times 8) \] \[ = 2(32 + 16 + 32) \] \[ = 2(80) = 160\ \text{cm}^2 \]
So Assertion (A) is true.

Step 2: Check Reason (R)
The correct surface area formula is:
\[ 2(lb + bh + hl) \] But Reason (R) states only \[ lb + bh + hl \] which is incorrect.

So Reason (R) is false.

Final Conclusion:
Assertion (A) is true.
Reason (R) is false.