Question

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

Reason (R): The surface area of a cuboid of dimensions $$l \times b \times h$$ is $$(lb + bh + lh)$$.

पर्याय

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. Joining the cubes end to end forms a cuboid of dimensions $$8\ \mathrm{cm} \times 4\ \mathrm{cm} \times 4\ \mathrm{cm}$$. Its surface area is: $$2(lb + bh + lh) = 2(8 \times 4 + 4 \times 4 + 8 \times 4) = 160\ \mathrm{cm}^{2}$$

Step 2 – Reason: R is false. The stated expression is missing the factor of 2; the surface area of a cuboid is $$2(lb + bh + lh)$$.

Therefore, the correct option is: Assertion (A) is true and Reason (R) is false.