Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A cuboidal block of 6 cm × 9 cm × 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be
(a)6
(b)9
(c)24
(d)30
Answer
Answer (as printed): C
Explanation
Volume of block $=(6 \times 9 \times 12) \mathrm{cm}^{3}=648 \mathrm{cm}^{3}$. Side of largest cube = H.C.F. of 6 cm, 9 cm, 12 cm $=3 \mathrm{cm} .$ Volume of this cube $=(3 \times 3 \times 3) \mathrm{cm}=27 \mathrm{cm}^{3}$. $$\text { ∴ Number of cubes }=\left(\frac{648}{27}\right)=24 .$$