Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The volume of a rectangular block of stone is 10368 $\mathrm{dm}^{3}$. Its dimensions are in the ratio of 3 : 2 : 1. If its entire surface is polished at 2 paise per $\mathrm{dm}^{2}$, then the total cost will be
(a)₹ 31.50
(b)₹ 31.68
(c)₹ 63
(d)₹ 63.36
Answer
Answer (as printed): D
Explanation
Let the dimensions be $3 x, 2 x$ and $x$ respectively. Then, $$3 x \times 2 x \times x=10368 \Leftrightarrow x^{3}=\left(\frac{10368}{6}\right)=1728 \Leftrightarrow x=12 .$$ So, the dimensions of the block are 36 dm, 24 dm and 12 dm. Surface area $=[2(36 \times 24+24 \times 12+36 \times 12)] \mathrm{dm}^{2}$ $$=[2 \times 144(6+2+3)] \mathrm{dm}^{2}=3168 \mathrm{dm}^{2} . \text { ∴ Cost of polishing }=₹\left(\frac{2 \times 3168}{100}\right)=₹ 63.36 .$$
Explanation as extracted from the printed page; notation may be imperfect.