Question

The volume of a rectangular block of stone is $10360d{m}^3.$ Its dimensions are in the ratio of $3:2:1$. If the entire surface is polished at $2$ paise per $d{m}^3$, then the total cost will be

• A. $Rs31.50$
• B. $Rs63.00$
• C. $Rs63.36$
• D. $Rs31.68$

Answer 1

Answer: (C)

$Rs63.36$

Let the length of the cuboid $=3x$, breadth $=2x$, height $=x$
Volume of a cuboid $=l\times b\times h$

Given, volume of the cuboid $=10368{dm}^3$

$=>3x\times 2x\times 2x=10368{dm}^3$

$=>6x^3=10368{dm}^3$

$=>x=12$

Hence, the length of the cuboid $=3x=36dm$, breadth $=2x=24dm$, height $=x=12dm$

Total surface area of a cuboid of $=2(l\times b+b\times h+l\times h)$
So, the total surface area of the cuboid $=2(36\times 24+24\times 12+12\times 36)=2\left(1584\right)=3168{dm}^2$

Cost of polishing at $2$ paise per ${dm}^2=3168\times 2=6336$ paise $=Rs63.36$