Question

A rectangular box must hold $60$ cubic decimetres of material. Its length, breadth and height are in the ratio $3:4:5$. We have to paint all the six of its surfaces. If the paint costs $10$ rupees per square metre, then the total cost of painting the box will be:

• A. $94$ paise
• B. Rs. $1.40$
• C. Rs. $9.40$
• D. Rs. $19.40$

Answer 1

The correct option is C Rs. $9.40$

Let the length,breadth and height of the box be $3x$ dm, $4x$ dm and $5x$ dm.

Then, $3x\times 4x\times 5x=60$
$\Rightarrow 60x^3=60$

$\Rightarrow x^3=1$

$\Rightarrow x=1$
$\therefore$ the dimensions of the box are $3$ dm, $4$ dm and $5$ dm, i.e., $0.3$ m, $0.4$ m, $0.5$ m.

Total surface area of the box
$=2(0.3\times 0.4+0.4\times 0.5+0.3\times 0.5)m^2$
$=2(0.12+0.2+0.15)m^2$
$=2\times 0.47m^2=0.94m^2$
$\therefore$ Total cost of painting $=$ Rs. $(10\times 0.94)$ $=$ Rs. $9.40$