3. Example problem of cuboid

A closed wooden box is in the form of a cuboid. Its length, breadth and height are $5 \ m$, $3 \ m$ and $150 \ cm$ respectively. Find the total surface area and the cost of painting its entire outer surface at the rate of $₹25$ per $m^2$.

 

 

Solution:

 

Length of the box $=$ $5 \ m$

 

Breadth of the box $=$ $3 \ m$

 

Height of the box $=$ $150 \ cm$ $=$ $\frac{150}{100}$ $=$$1.5 \ m$

 

Total surface area $=$ $2 (lb + bh + lh)$

 

$=$ $2 ((5 \times 3) + (3 \times 1.5) + (5 \times 1.5))$

 

$=$ $2 (15 + 4.5 + 7.5)$

 

$=$ $2 (27)$

 

$=$ $54 \ m^2$

 

Total surface area of the box is $54 \ m^2$.

 

Cost of painting per $m^2$ $=$ $₹25$

 

Cost of painting for $54 \ m^2$:

 

$=$ $54 \times 25$

 

$=$ $1350$

 

Cost of painting the entire outer surface area of the box is $₹1350$.