Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A cube of white chalk is painted red, and then cut parallel to the sides to form two rectangular solids of equal volumes. What percent of the surface area of each of the new solids is not painted red?
(a)15\%
(b)$16 \frac{2}{3} \%$
(c)20\%
(d)25\%
Answer
Answer (as printed): D
Explanation
Let the length of each edge of the cube be $a$. Then, the dimensions of each of the two rectangular solids are $a, a$ and $\frac{a}{2}$. Surface area of each rectangular solid $$=2\left[a \times a+a \times \frac{a}{2}+a \times \frac{a}{2}\right]=4 a^{2} .$$ Surface area of unpainted face of each solid $$=(a \times a)=a^{2} .$$ ∴ Required percentage $=\left(\frac{a^{2}}{4 a^{2}} \times 100\right) \%=25 \%$.
Explanation as extracted from the printed page; notation may be imperfect.