**Assertion (A) :** The surface area of the cuboid formed by joinin...

Question

**Assertion (A) :** The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm$^2$.

**Reason (R) :** The surface area of a cuboid of dimensions $l 	imes b 	imes h$ is $(lb + bh + hl)$.

Accepted Answer

**Step 1 — Check the Assertion (A).**
Joining two cubes of edge 4 cm end-to-end gives a cuboid of dimensions
$$l = 8 	ext{ cm}, \quad b = 4 	ext{ cm}, \quad h = 4 	ext{ cm}$$

Total surface area
$$= 2(lb + bh + hl) = 2(8	imes4 + 4	imes4 + 4	imes8)$$
$$= 2(32 + 16 + 32) = 2 	imes 80 = 160 	ext{ cm}^2$$

$	herefore$ **Assertion (A) is TRUE.**

**Step 2 — Check the Reason (R).**
The correct formula is
$$	ext{TSA of cuboid} = \mathbf{2}(lb + bh + hl)$$
The Reason omits the factor $2$.

$	herefore$ **Reason (R) is FALSE.**

**Step 3 — Choose the option.**
Assertion true, Reason false.

**Answer : (C)**

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