Which of the following statements are true?
(A) If the diagonal of a cube is $6\sqrt{3} cm$, then its volume and surface area are equal.
(B) If a rectangular block having dimensions 6 cm × 12 cm × 15 cm is cut into an exact number of equal cubes, then the least possible number of such cubes is 27.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) only
Let us verify each statement.
Statement (A)
Diagonal of a cube $= a\sqrt{3}$
Given:
$a\sqrt{3} = 6\sqrt{3} \Rightarrow a = 6 \text{ cm}$
- Volume $= a^3 = 6^3 = 216$
- Surface area $= 6a^2 = 6 \times 36 = 216$
Volume = Surface area
Statement (A) is true
Statement (B)
Dimensions of cuboid = $6 \times 12 \times 15$
Side of largest possible cube = HCF of $6,12,15=3$ cm
Number of cubes:
$\frac{6}{3} \times \frac{12}{3} \times \frac{15}{3} = 2 \times 4 \times 5 = 40$
Least possible number of cubes = 40, not 27.
Statement (B) is false
Correct Answer: (A) only