Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes will be
(a)1 : 3
(b)2 : 3
(c)5 : 9
(d)7 : 9
Answer
Answer (as printed): D
Explanation
Let the length of each edge of each cube be $a$. Then, the cuboid formed by placing 3 cubes adjacently has the dimensions $3 a, a$ and $a$. Surface area of the cuboid $=2[3 a \times a+a \times a+3 a \times a]$ $$=2\left(3 a^{2}+a^{2}+3 a^{2}\right)=14 a^{2} .$$ Sum of surface areas of 3 cubes $=\left(3 \times 6 a^{2}\right)=18 a^{2}$. ∴ Required ratio $=14 a^{2}: 18 a^{2}=7: 9$.
Explanation as extracted from the printed page; notation may be imperfect.