Question

A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given cube and that of one of the cuboids.

• A. $3:2$
• B. $2:1$
• C. $1:2$
• D. $2:3$

Answer 1

Answer: (A)

$3:2$

Let the side of the cube be $a$.

Total surface area of a cube$=6a^2$

Length of the each resulting cuboid is half of the side of the cube $=\frac{a}{2}$.

Height and breadth of the cuboid remain same as the side of the cube $a$.

Total surface area of a cuboid $=2(l\times b+b\times h+l\times h)$$=2(\frac{a}{2}\times a+a\times a+\frac{a}{2}\times a)=4a^2$

Ratio of the total surface area of the given cube and that of one of the cuboids $=6a^2:4a^2=3:2$