Question

Directions: In the following question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion: Two equal cubes are placed adjacent in a row. The ratio of total surface area of the new cuboid to that of the sum of the surface areas of two cubes is 5 : 6

Reason: Surface Area of a cube is $6sid{e}^2$.

• A. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
• B. Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
• C. Assertion (A) is true but reason (R) is false.
• D. Assertion (A) is false but reason (R) is true.

Answer 1

The correct option is A Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(A) The resultant shape obtained is a cuboid


Let, side of cube = a units

surface area of the cube = 6a${}^2$ square units

sum of surface areas of two cubes = 12a${}^2$---(i)

If two cubes are joined end to end then cuboid Dimensions are

length = l = 2a
breadth = b = a
height = h = a

total surface area of the cuboid =2(lb + bh + lh)

$=2(2a\times a+a\times a+2a\times a)$

$=2\left(5a^2\right)$

$=10a^2$--- (ii)

required ratio = (ii) ÷ (i)

$=\frac{10}{12}$

$=\frac{5}{6}$

$=5:6$

So that Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).