Question

A solid cube is cut into two cuboids exactly at middle as shown in figure. Find the ratio of the total surface area of the given cube and that of the cuboid.

• A. $3:2$
• B. $2:5$
• C. $5:7$
• D. $6:1$

Answer 1

The correct option is A $3:2$

Given, A solid cube is cut at middle to make two make two cuboids.
Let the side of the cube be $a$ and it is cut at middle. So breadth of newly formed cuboids is ($a$/2), length is$a$, height is $a$.
Total surface area of cube$=6a^2$
Total surface area of cuboids $=$ Surface area of cuboid
$=2(lb+bh+lh)=2(\frac{a}{2}\times a+a\times a+\frac{a}{2}\times a)=4a^2$
Ratio of total surface area of cube to cuboid $=\frac{6a^2}{4a^2}=3:2$