Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu. cm; then the length of the shortest side is
(a)10 cm
(b)15 cm
(c)20 cm
(d)30 cm
Answer
Answer (as printed): B
Explanation
Let $l b=2 x, b h=3 x$ and $l h=4 x$. Then, $24 x^{3}=(l b h)^{2}=9000 \times 9000 \Rightarrow x^{3}=375 \times 9000$ $$\Rightarrow x=150 .$$ So, $l b=300, b h=450, l h=600$ and $l b h=9000$. $$\therefore h=\frac{9000}{300}=30, l=\frac{9000}{450}=20 \text { and } b=\frac{9000}{600}=15 .$$ Hence, shortest side = 15 cm.
Explanation as extracted from the printed page; notation may be imperfect.